Sin^ 4 (x)+cos^4 (x)=1

Question

Sin^ 4 (x)+cos^4 (x)=1

Answer 1

(1-cos2x)²/4+(1+cos2x)²/4=1
1-2cos2x+cos²2x+1+2cos2x+cos²2x=4
2cos²2x=2
cos²2x=1
(1+cos4x)/2=1
1+cos4x=2
cos4x=1
4x=2πn
x=πn/2,n∈z