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

The general solution for sin^4(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin

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sin^4(x)=1

sin^{4} (x) = 1

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{4} (x) = 1

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = i :

No Solution

sin (x) = - i :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin (x) cos (x) + 2 sin (x) = 0, 0 \leq x < 2 π

(cos (x) + 1) = 0

cos (x) = - 1, sin (x)

3 cos (2 θ) - 5 cos (θ) = 1

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

What is the general solution for sin^4(x)=1 ?
The general solution for sin^4(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin