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

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

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tan^4(x)=tan(x)

tan^{4} (x) = tan (x)

x = πn, x = \frac{π}{4} + πn

Solution steps

tan^{4} (x) = tan (x)

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = 1 : x = \frac{π}{4} + πn

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

No Solution

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

No Solution

Combine all the solutions

x = πn, x = \frac{π}{4} + πn

2 sin (θ) - csc (θ) = 1

\frac{sin ( 2 x )}{4 sin ( 2 x ) - 1} = 1

arctan (x) = 119.74

2 cos (θ) sin (θ) = sin (θ)

4 cos (x) = sec (x)

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