What is the general solution for tan^7(x)=tan(x) ?

The general solution for tan^7(x)=tan(x) is x=pin,x=(3pi)/4+pin,x= pi/4+pin

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tan^7(x)=tan(x)

tan^{7} (x) = tan (x)

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

tan^{7} (x) = tan (x)

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

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

No Solution

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

No Solution

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

No Solution

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

No Solution

Combine all the solutions

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

tan (x) = \frac{1}{6}

cos (2 x) = 5 sin (x) - 2

tan (θ) = 0.48

2 sec (x) tan (x) + 2 sec (x) + tan (x) + 1 = 0

6 tan^{2} (θ) cos (θ) + 3 tan^{2} (θ) = 0

What is the general solution for tan^7(x)=tan(x) ?
The general solution for tan^7(x)=tan(x) is x=pin,x=(3pi)/4+pin,x= pi/4+pin