Solve for x if (-sin x)^4+(cos x)^4 =1. Please explain with all steps.

To solve (-sinx)^4 + (cosx)^4 =
1:

We know (cosx)^2 +(sinx)^2 = 1 , the trigonometric
 identy.

To solve the equation we put on the right 1=
{(sinx)^2+(cosx)^2}^2.

Then (-sinx)^4 +(cosx)^4 =
{(sinx)^2+(cosx)^2}^2.

Then (sinx)^4 + (cosx)^4 = (cosx)^4
+  2(sinx)^2*(cosx)^2 +(cosx)^4 , as the coefficient (-1)^4 = 
1.

0 = 2(sinx)^2 (cosx)^2. Other terms
cancel.

(sinx)^2 = 0. Or( cosx)^2 =
0

sinx = 0. Or cosx =  0

sinx
= 0 gives: x =  npi, n =0,1,2,...

cosx = 0 gives: x = (2n +
or - 1)pi  , n = 0, 1,2,.