Sin^2x-cos^2x=cos^22x

Question

Sin^2x-cos^2x=cos^22x

Answer 1

Sin²x-cos²x=cos²2x
-cos²2x=cos²2x
cos²2x+cos2x=0
cos2x(cos2x+1)=0
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
cos2x=-1⇒2x=π+2πn⇒x=π/2+πn