Sin2x=cos^4x/2-sin^4x/2

Question

Sin2x=cos^4x/2-sin^4x/2

Answer 1

Sin2x=(cos²x/2-sin²x/2)(cos²x/2+sin²x/2)
sin2x=cosx
2sinxcosx-cosx=0
cosx(2sinx-1)=0
cosx=0⇒x=π/2+πn
sinx=1/2⇒x=(-1)^n *π/6+πn