What is the general solution for 9tan(x/2)+7=5tan(x/2)+3 ?

The general solution for 9tan(x/2)+7=5tan(x/2)+3 is x=(3pi)/2+2pin

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Popular Trigonometry >

9tan(x/2)+7=5tan(x/2)+3

Solution

9 tan (\frac{x}{2}) + 7 = 5 tan (\frac{x}{2}) + 3

Solution

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

9 tan (\frac{x}{2}) + 7 = 5 tan (\frac{x}{2}) + 3

Solve by substitution

9 tan (\frac{x}{2}) + 7 = 5 tan (\frac{x}{2}) + 3

Let:

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

9 u + 7 = 5 u + 3

9 u + 7 = 5 u + 3 : u = - 1

9 u + 7 = 5 u + 3

Move

7

to the right side

9 u + 7 = 5 u + 3

Subtract

7

from both sides

9 u + 7 - 7 = 5 u + 3 - 7

Simplify

9 u = 5 u - 4

9 u = 5 u - 4

Move

5 u

to the left side

9 u = 5 u - 4

Subtract

5 u

from both sides

9 u - 5 u = 5 u - 4 - 5 u

Simplify

4 u = - 4

4 u = - 4

Divide both sides by

4

4 u = - 4

Divide both sides by

4

\frac{4 u}{4} = \frac{- 4}{4}

Simplify

u = - 1

u = - 1

Substitute back

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

tan (\frac{x}{2}) = - 1

tan (\frac{x}{2}) = - 1

tan (\frac{x}{2}) = - 1 : x = \frac{3 π}{2} + 2 πn

tan (\frac{x}{2}) = - 1

General solutions for

tan (\frac{x}{2}) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{x}{2} = \frac{3 π}{4} + πn

\frac{x}{2} = \frac{3 π}{4} + πn

Solve

\frac{x}{2} = \frac{3 π}{4} + πn : x = \frac{3 π}{2} + 2 πn

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{3 π}{4} + 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{3 π}{4} + 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{3 π}{4} + 2 πn : \frac{3 π}{2} + 2 πn

2 \cdot \frac{3 π}{4} + 2 πn

2 \cdot \frac{3 π}{4} = \frac{3 π}{2}

2 \cdot \frac{3 π}{4}

Multiply fractions:

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

= \frac{3 π 2}{4}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 π}{4}

Cancel the common factor:

2

= \frac{3 π}{2}

= \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

Graph

Popular Examples

(1-tanh(2x))/(1+tanh(2x))=2

Frequently Asked Questions (FAQ)

What is the general solution for 9tan(x/2)+7=5tan(x/2)+3 ?
The general solution for 9tan(x/2)+7=5tan(x/2)+3 is x=(3pi)/2+2pin