Question

Solve cos^2(2x)-sin^2(2x)=sqrt3/2

Answer 1

`\cos^22x-\sin^22x=(\sqrt3)/(2)\\\\\cos(4x)=(\sqrt3)/(2)\iff4x=30^o\to x=7.5^o\\----------------------\\\cos^22x-\sin^22x=(\sqrt3)/(2)\\\\\cos(4x)=(\sqrt3)/(2)\iff4x=(\pi)/(6)+2k\pi\ or\ 4x=-(\pi)/(6)+2k\pi\\\\\boxed{x=(\pi)/(24)+(k\pi)/(2)\ or\ x=-(\pi)/(24)+(k\pi)/(2)\ for\ k\in\mathbb{Z}}`