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

The general solution for tan(4x)-tan(2x)=0 is x=pin,x= pi/2+pin

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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

t, sin (t) + 2 sin (2 t) = 0

tan^{2} (x) - sin (x) tan^{2} (x) = 0

- 1 - tan (x) = sec (x), 0 \leq x < 2 π

cosh (z) + 1 = 0

tan (x) = 11, sin (x)

What is the general solution for tan(4x)-tan(2x)=0 ?
The general solution for tan(4x)-tan(2x)=0 is x=pin,x= pi/2+pin