What is the general solution for (tan(3x))/(tan(2x))=1 ?

The general solution for (tan(3x))/(tan(2x))=1 is No Solution for x\in\mathbb{R}

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(tan(3x))/(tan(2x))=1

\frac{tan ( 3 x )}{tan ( 2 x )} = 1

No Solution for x \in R

Solution steps

\frac{tan ( 3 x )}{tan ( 2 x )} = 1

Subtract

1

from both sides

\frac{tan ( 3 x )}{tan ( 2 x )} - 1 = 0

Simplify

\frac{tan ( 3 x )}{tan ( 2 x )} - 1 : \frac{tan ( 3 x ) - tan ( 2 x )}{tan ( 2 x )}

\frac{tan ( 3 x ) - tan ( 2 x )}{tan ( 2 x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (3 x) - tan (2 x) = 0

Express with sin, cos

\frac{cos ( 2 x ) sin ( 3 x ) - cos ( 3 x ) sin ( 2 x )}{cos ( 2 x ) cos ( 3 x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (2 x) sin (3 x) - cos (3 x) sin (2 x) = 0

Rewrite using trig identities

sin (3 x - 2 x) = 0

General solutions for

sin (3 x - 2 x) = 0

3 x - 2 x = 0 + 2 πn, 3 x - 2 x = π + 2 πn

Solve

3 x - 2 x = 0 + 2 πn : x = 2 πn

Solve

3 x - 2 x = π + 2 πn : x = π + 2 πn

x = 2 πn, x = π + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

No Solution for x \in R

6 cot (x) = 5 - tan (x)

3 cos (θ) - 3 = 0

(3 tan (x) - 1) (tan (x) - 3) = 0

sin (X) = \frac{2}{2}

x, 2 + sin (x) = 0

What is the general solution for (tan(3x))/(tan(2x))=1 ?
The general solution for (tan(3x))/(tan(2x))=1 is No Solution for x\in\mathbb{R}