What is the general solution for tan(4x)=tan(2x) ?

The general solution for tan(4x)=tan(2x) is x=pin,x= pi/2+pin

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tan(4x)=tan(2x)

tan (4 x) = tan (2 x)

x = πn, x = \frac{π}{2} + πn

Solution steps

tan (4 x) = tan (2 x)

Subtract

tan (2 x)

from both sides

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

Express with sin, cos

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

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

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

Rewrite using trig identities

sin (4 x - 2 x) = 0

General solutions for

sin (4 x - 2 x) = 0

4 x - 2 x = 0 + 2 πn, 4 x - 2 x = π + 2 πn

Solve

4 x - 2 x = 0 + 2 πn : x = πn

Solve

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

x = πn, x = \frac{π}{2} + πn

x, cos (2 x + 5 x) = cos (H x)

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

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

3 sin (x) = sin (x) tan (x)

- 2 sin (2 y) = 0

What is the general solution for tan(4x)=tan(2x) ?
The general solution for tan(4x)=tan(2x) is x=pin,x= pi/2+pin