What is the general solution for 4cos(2x)-2sin(2x)=0 ?

The general solution for 4cos(2x)-2sin(2x)=0 is x=(1.10714…)/2+(pin)/2

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Popular >

4cos(2x)-2sin(2x)=0

Solution

4 cos (2 x) - 2 sin (2 x) = 0

Solution

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

Degrees

x = 31.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

4 cos (2 x) - 2 sin (2 x) = 0

Rewrite using trig identities

4 cos (2 x) - 2 sin (2 x) = 0

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

\frac{4 cos ( 2 x ) - 2 sin ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

4 - \frac{2 sin ( 2 x )}{cos ( 2 x )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

4 - 2 tan (2 x) = 0

4 - 2 tan (2 x) = 0

Move

4

to the right side

4 - 2 tan (2 x) = 0

Subtract

4

from both sides

4 - 2 tan (2 x) - 4 = 0 - 4

Simplify

- 2 tan (2 x) = - 4

- 2 tan (2 x) = - 4

Divide both sides by

- 2

- 2 tan (2 x) = - 4

Divide both sides by

- 2

\frac{- 2 tan ( 2 x )}{- 2} = \frac{- 4}{- 2}

Simplify

\frac{- 2 tan ( 2 x )}{- 2} = \frac{- 4}{- 2}

Simplify

\frac{- 2 tan ( 2 x )}{- 2} : tan (2 x)

\frac{- 2 tan ( 2 x )}{- 2}

Apply the fraction rule:

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

= \frac{2 tan ( 2 x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= tan (2 x)

Simplify

\frac{- 4}{- 2} : 2

\frac{- 4}{- 2}

Apply the fraction rule:

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

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

tan (2 x) = 2

tan (2 x) = 2

tan (2 x) = 2

Apply trig inverse properties

tan (2 x) = 2

General solutions for

tan (2 x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x = arctan (2) + πn

2 x = arctan (2) + πn

Solve

2 x = arctan (2) + πn : x = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

2 x = arctan (2) + πn

Divide both sides by

2

2 x = arctan (2) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

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3 cot (θ) = 3

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sec (x) = 1, - 2 π \leq x \leq 2 π

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tan (t) = \frac{4}{3}, sin (t)

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Frequently Asked Questions (FAQ)

What is the general solution for 4cos(2x)-2sin(2x)=0 ?
The general solution for 4cos(2x)-2sin(2x)=0 is x=(1.10714…)/2+(pin)/2