Sin^4 x + cos^4 x = cos4x

(1-cos2x)²/4+(1+cos2x)²/4=cos4x2+2cos²2x=4cos4x2+2cos²2x=8cos²2x-48cos²2x-2cos2x-6=04cos²2x-cos2x-3=0cos2x=a4a²-a-3=0D=1+48=49a1=(1-7)/8=-3/4⇒cos2x=-3/4⇒x=+-1/2arccos3/4+2πna2=(1+7)/8=1⇒cos2x=1⇒x=πn