Question

СРОЧНО ПОМОГИТЕ! cos^4x+sin^4x=cos4x

Answer 1

(1+сos2x)²/4+(1-cos2x)²/4=cos4x
1+2cos2x+cos²2x+1-2cos2x+cos²2x=4cos4x
2+2cos²2x=4cos4x
1+cos²2x=2cos4x
4cos²2x-2-cos²2x-1=0
3cos²2x-3=0
3(cos²2x-1)=0
cos²2x=1
(1+cos4x)/2=1
1+cos4x=2
cos4x=1
4x=2πn,n∈z
x=πn/2,n∈z