What is the general solution for sin(2x+15)=cos(1/2 x-15) ?

The general solution for sin(2x+15)=cos(1/2 x-15) is No Solution for x\in\mathbb{R}

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Popular Trigonometry >

sin(2x+15)=cos(1/2 x-15)

Solution

sin (2 x + 1 5^{\circ}) = cos (\frac{1}{2} x - 1 5^{\circ})

Solution

No Solution for x \in R

Solution steps

sin (2 x + 1 5^{\circ}) = cos (\frac{1}{2} x - 1 5^{\circ})

Rewrite using trig identities

sin (2 x + 1 5^{\circ}) = cos (\frac{1}{2} x - 1 5^{\circ})

Use the following identity:

cos (x) = sin (9 0^{\circ} - x)

sin (2 x + 1 5^{\circ}) = sin (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}))

sin (2 x + 1 5^{\circ}) = sin (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}))

Apply trig inverse properties

sin (2 x + 1 5^{\circ}) = sin (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}))

sin (x) = sin (y) \Rightarrow x = y + 2 π n, x = π - y + 2 π n

2 x + 1 5^{\circ} = 9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n, 2 x + 1 5^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n

2 x + 1 5^{\circ} = 9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n, 2 x + 1 5^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n

2 x + 1 5^{\circ} = 9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n : x = \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

2 x + 1 5^{\circ} = 9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n

Expand

9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n : 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ}

9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) + 36 0^{\circ} n

- (\frac{1}{2} x - 1 5^{\circ}) : - \frac{1}{2} x + 1 5^{\circ}

- (\frac{1}{2} x - 1 5^{\circ})

Distribute parentheses

= - (\frac{1}{2} x) - (- 1 5^{\circ})

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - \frac{1}{2} x + 1 5^{\circ}

= 9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ} + 36 0^{\circ} n

Simplify

9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ} + 36 0^{\circ} n : 36 0^{\circ} n + \frac{- 6 x + 126 0 ^{\circ}}{12}

9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ} + 36 0^{\circ} n

Group like terms

= - \frac{1}{2} x + 36 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

Multiply

\frac{1}{2} x : \frac{x}{2}

\frac{1}{2} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x}{2}

Multiply:

1 \cdot x = x

= \frac{x}{2}

= - \frac{x}{2} + 36 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

Least Common Multiplier of

2, 2, 12 : 12

2, 2, 12

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Compute a number comprised of factors that appear in at least one of the following:

2, 2, 12

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

12

For

\frac{x}{2} :

multiply the denominator and numerator by

6

\frac{x}{2} = \frac{x \cdot 6}{2 \cdot 6} = \frac{x \cdot 6}{12}

For

9 0^{\circ} :

multiply the denominator and numerator by

6

9 0^{\circ} = \frac{18 0 ^{\circ} 6}{2 \cdot 6} = 9 0^{\circ}

= - \frac{x \cdot 6}{12} + 9 0^{\circ} + 1 5^{\circ}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- x \cdot 6 + 18 0 ^{\circ} 6 + 18 0 ^{\circ}}{12}

Add similar elements:

108 0^{\circ} + 18 0^{\circ} = 126 0^{\circ}

= 36 0^{\circ} n + \frac{- 6 x + 126 0 ^{\circ}}{12}

= 36 0^{\circ} n + \frac{- 6 x + 126 0 ^{\circ}}{12}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- x \cdot 6 + 126 0 ^{\circ}}{12} = - \frac{x \cdot 6}{12} + 10 5^{\circ}

= 36 0^{\circ} n - \frac{6 x}{12} + 10 5^{\circ}

Cancel

\frac{x \cdot 6}{12} : \frac{x}{2}

\frac{x \cdot 6}{12}

Cancel the common factor:

6

= \frac{x}{2}

= 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ}

2 x + 1 5^{\circ} = 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ}

Move

1 5^{\circ}

to the right side

2 x + 1 5^{\circ} = 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ}

Subtract

1 5^{\circ}

from both sides

2 x + 1 5^{\circ} - 1 5^{\circ} = 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ} - 1 5^{\circ}

Simplify

2 x + 1 5^{\circ} - 1 5^{\circ} = 36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ} - 1 5^{\circ}

Simplify

2 x + 1 5^{\circ} - 1 5^{\circ} : 2 x

2 x + 1 5^{\circ} - 1 5^{\circ}

Add similar elements:

1 5^{\circ} - 1 5^{\circ} = 0

= 2 x

Simplify

36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ} - 1 5^{\circ} : 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

36 0^{\circ} n - \frac{x}{2} + 10 5^{\circ} - 1 5^{\circ}

Combine the fractions

10 5^{\circ} - 1 5^{\circ} : 9 0^{\circ}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{126 0 ^{\circ} - 18 0 ^{\circ}}{12}

Add similar elements:

126 0^{\circ} - 18 0^{\circ} = 108 0^{\circ}

= 9 0^{\circ}

Cancel the common factor:

6

= 9 0^{\circ}

= 36 0^{\circ} n - \frac{x}{2} + 9 0^{\circ}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

2 x = 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

2 x = 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

2 x = 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

Multiply both sides by

2

2 x = 36 0^{\circ} n + \frac{- x + 18 0 ^{\circ}}{2}

Multiply both sides by

2

2 x \cdot 2 = 36 0^{\circ} n \cdot 2 + \frac{- x + 18 0 ^{\circ}}{2} \cdot 2

Simplify

2 x \cdot 2 = 36 0^{\circ} n \cdot 2 + \frac{- x + 18 0 ^{\circ}}{2} \cdot 2

Simplify

2 x \cdot 2 : 4 x

2 x \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4 x

Simplify

36 0^{\circ} n \cdot 2 : 72 0^{\circ} n

36 0^{\circ} n \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 72 0^{\circ} n

Simplify

\frac{- x + 18 0 ^{\circ}}{2} \cdot 2 : - x + 18 0^{\circ}

\frac{- x + 18 0 ^{\circ}}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - x + 18 0 ^{\circ} ) \cdot 2}{2}

Cancel the common factor:

2

= - - x + 18 0^{\circ}

4 x = 72 0^{\circ} n - x + 18 0^{\circ}

4 x = 72 0^{\circ} n - x + 18 0^{\circ}

4 x = 72 0^{\circ} n - x + 18 0^{\circ}

Move

x

to the left side

4 x = 72 0^{\circ} n - x + 18 0^{\circ}

Add

x

to both sides

4 x + x = 72 0^{\circ} n - x + 18 0^{\circ} + x

Simplify

5 x = 72 0^{\circ} n + 18 0^{\circ}

5 x = 72 0^{\circ} n + 18 0^{\circ}

Divide both sides by

5

5 x = 72 0^{\circ} n + 18 0^{\circ}

Divide both sides by

5

\frac{5 x}{5} = \frac{72 0 ^{\circ} n}{5} + 3 6^{\circ}

Simplify

\frac{5 x}{5} = \frac{72 0 ^{\circ} n}{5} + 3 6^{\circ}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{72 0 ^{\circ} n}{5} + 3 6^{\circ} : \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

\frac{72 0 ^{\circ} n}{5} + 3 6^{\circ}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

x = \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

x = \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

x = \frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}

2 x + 1 5^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n : x = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

2 x + 1 5^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n

Expand

18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n : 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})) + 36 0^{\circ} n

Expand

9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ}) : \frac{- x \cdot 6 + 126 0 ^{\circ}}{12}

9 0^{\circ} - (\frac{1}{2} x - 1 5^{\circ})

- (\frac{1}{2} x - 1 5^{\circ}) : - \frac{1}{2} x + 1 5^{\circ}

- (\frac{1}{2} x - 1 5^{\circ})

Distribute parentheses

= - (\frac{1}{2} x) - (- 1 5^{\circ})

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - \frac{1}{2} x + 1 5^{\circ}

= 9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ}

Simplify

9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ} : \frac{- 6 x + 126 0 ^{\circ}}{12}

9 0^{\circ} - \frac{1}{2} x + 1 5^{\circ}

Group like terms

= - \frac{1}{2} x + 9 0^{\circ} + 1 5^{\circ}

Multiply

\frac{1}{2} x : \frac{x}{2}

\frac{1}{2} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x}{2}

Multiply:

1 \cdot x = x

= \frac{x}{2}

= - \frac{x}{2} + 9 0^{\circ} + 1 5^{\circ}

Least Common Multiplier of

2, 2, 12 : 12

2, 2, 12

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Compute a number comprised of factors that appear in at least one of the following:

2, 2, 12

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

12

For

\frac{x}{2} :

multiply the denominator and numerator by

6

\frac{x}{2} = \frac{x \cdot 6}{2 \cdot 6} = \frac{x \cdot 6}{12}

For

9 0^{\circ} :

multiply the denominator and numerator by

6

9 0^{\circ} = \frac{18 0 ^{\circ} 6}{2 \cdot 6} = 9 0^{\circ}

= - \frac{x \cdot 6}{12} + 9 0^{\circ} + 1 5^{\circ}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- x \cdot 6 + 18 0 ^{\circ} 6 + 18 0 ^{\circ}}{12}

Add similar elements:

108 0^{\circ} + 18 0^{\circ} = 126 0^{\circ}

= \frac{- 6 x + 126 0 ^{\circ}}{12}

= \frac{- 6 x + 126 0 ^{\circ}}{12}

= 18 0^{\circ} - \frac{- 6 x + 126 0 ^{\circ}}{12} + 36 0^{\circ} n

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- x \cdot 6 + 126 0 ^{\circ}}{12} = - (- \frac{x \cdot 6}{12}) - (10 5^{\circ})

= 18 0^{\circ} - (- \frac{6 x}{12}) - (10 5^{\circ}) + 36 0^{\circ} n

Remove parentheses:

(a) = a, - (- a) = a

= 18 0^{\circ} + \frac{x \cdot 6}{12} - 10 5^{\circ} + 36 0^{\circ} n

Cancel

\frac{x \cdot 6}{12} : \frac{x}{2}

\frac{x \cdot 6}{12}

Cancel the common factor:

6

= \frac{x}{2}

= 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n

2 x + 1 5^{\circ} = 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n

Move

1 5^{\circ}

to the right side

2 x + 1 5^{\circ} = 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n

Subtract

1 5^{\circ}

from both sides

2 x + 1 5^{\circ} - 1 5^{\circ} = 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n - 1 5^{\circ}

Simplify

2 x + 1 5^{\circ} - 1 5^{\circ} = 18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n - 1 5^{\circ}

Simplify

2 x + 1 5^{\circ} - 1 5^{\circ} : 2 x

2 x + 1 5^{\circ} - 1 5^{\circ}

Add similar elements:

1 5^{\circ} - 1 5^{\circ} = 0

= 2 x

Simplify

18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n - 1 5^{\circ} : \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

18 0^{\circ} + \frac{x}{2} - 10 5^{\circ} + 36 0^{\circ} n - 1 5^{\circ}

Group like terms

= \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 1 5^{\circ} - 10 5^{\circ}

Combine the fractions

- 1 5^{\circ} - 10 5^{\circ} : - 12 0^{\circ}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 18 0 ^{\circ} - 126 0 ^{\circ}}{12}

Add similar elements:

- 18 0^{\circ} - 126 0^{\circ} = - 144 0^{\circ}

= \frac{- 144 0 ^{\circ}}{12}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - 12 0^{\circ}

Cancel the common factor:

4

= - 12 0^{\circ}

= \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

2 x = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

2 x = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

2 x = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

Move

\frac{x}{2}

to the left side

2 x = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

Subtract

\frac{x}{2}

from both sides

2 x - \frac{x}{2} = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ} - \frac{x}{2}

Simplify

2 x - \frac{x}{2} = \frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ} - \frac{x}{2}

Simplify

2 x - \frac{x}{2} : \frac{3 x}{2}

2 x - \frac{x}{2}

Convert element to fraction:

2 x = \frac{2 x 2}{2}

= - \frac{x}{2} + \frac{2 x \cdot 2}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- x + 2 x \cdot 2}{2}

- x + 2 x \cdot 2 = 3 x

- x + 2 x \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= - x + 4 x

Add similar elements:

- x + 4 x = 3 x

= 3 x

= \frac{3 x}{2}

Simplify

\frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ} - \frac{x}{2} : 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

\frac{x}{2} + 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ} - \frac{x}{2}

Add similar elements:

\frac{x}{2} - \frac{x}{2} = 0

= 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

Multiply both sides by

2

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 12 0^{\circ}

Multiply both sides by

2

\frac{2 \cdot 3 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 12 0^{\circ}

Simplify

\frac{2 \cdot 3 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 12 0^{\circ}

Simplify

\frac{2 \cdot 3 x}{2} : 3 x

\frac{2 \cdot 3 x}{2}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{6 x}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3 x

Simplify

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 12 0^{\circ} : 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 12 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiply the numbers:

2 \cdot 2 = 4

= 72 0^{\circ} n

2 \cdot 12 0^{\circ} = 24 0^{\circ}

2 \cdot 12 0^{\circ}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 24 0^{\circ}

Multiply the numbers:

2 \cdot 2 = 4

= 24 0^{\circ}

= 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

Divide both sides by

3

3 x = 36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

Divide both sides by

3

\frac{3 x}{3} = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{24 0 ^{\circ}}{3}

Simplify

\frac{3 x}{3} = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{24 0 ^{\circ}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{24 0 ^{\circ}}{3} : \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{24 0 ^{\circ}}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{36 0 ^{\circ} + 72 0 ^{\circ} n - 24 0 ^{\circ}}{3}

Join

36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ} : \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{3}

36 0^{\circ} + 72 0^{\circ} n - 24 0^{\circ}

Convert element to fraction:

36 0^{\circ} = 36 0^{\circ}, 72 0^{\circ} n = \frac{72 0 ^{\circ} n 3}{3}

= 36 0^{\circ} + \frac{72 0 ^{\circ} n \cdot 3}{3} - 24 0^{\circ}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{36 0 ^{\circ} 3 + 72 0 ^{\circ} n \cdot 3 - 72 0 ^{\circ}}{3}

36 0^{\circ} 3 + 72 0^{\circ} n \cdot 3 - 72 0^{\circ} = 36 0^{\circ} + 216 0^{\circ} n

36 0^{\circ} 3 + 72 0^{\circ} n \cdot 3 - 72 0^{\circ}

Multiply the numbers:

2 \cdot 3 = 6

= 108 0^{\circ} + 4 \cdot 54 0^{\circ} n - 72 0^{\circ}

Multiply the numbers:

4 \cdot 3 = 12

= 108 0^{\circ} + 216 0^{\circ} n - 72 0^{\circ}

Group like terms

= 108 0^{\circ} - 72 0^{\circ} + 216 0^{\circ} n

Add similar elements:

108 0^{\circ} - 72 0^{\circ} = 36 0^{\circ}

= 36 0^{\circ} + 216 0^{\circ} n

= \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{3}

= \frac{\frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{3}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

x = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

x = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

x = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

Since the equation is undefined for:

\frac{72 0 ^{\circ} n + 18 0 ^{\circ}}{5}, \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sin(2x+15)=cos(1/2 x-15) ?
The general solution for sin(2x+15)=cos(1/2 x-15) is No Solution for x\in\mathbb{R}