Help pop Sin^4 x/2+cos^2x=2

Question

Help pop
Sin^4 x/2+cos^2x=2

Answer 1

Sin^4x/2+1+cos2x/2=2
sin^4x+1+cos2x=1
sin^4x+1+cos^2x-sin^2x=1
sin^4x+1+1-sin^2x-sin^2x-1=0
sin^4x-2sin^2x+1=0
sin^2x=a
a^2-2a+1=0
D=0
a=1
sin^2x=1
2x=п/2+2пк
х=п/4+пк, к€Z