What is the general solution for tan^4(x)=1 ?

The general solution for tan^4(x)=1 is x= pi/4+pin,x=(3pi)/4+pin

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tan^4(x)=1

tan^{4} (x) = 1

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

Solution steps

tan^{4} (x) = 1

Solve by substitution

tan (x) = 1, tan (x) = - 1, tan (x) = i, tan (x) = - i

tan (x) = 1 : x = \frac{π}{4} + πn

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

tan (x) = i :

No Solution

tan (x) = - i :

No Solution

Combine all the solutions

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

5 sin (x) cos (x) = cos (x)

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3 (2 sin (x) - 2) (4 cos (x) - 2) = 0

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

3 tan (θ) - 2 sin (θ) tan (θ) = 0

What is the general solution for tan^4(x)=1 ?
The general solution for tan^4(x)=1 is x= pi/4+pin,x=(3pi)/4+pin