Question

Cos 2x cos x - sin 2x sin x = 1/sqrt 2

Answer 1

$\cos2x\cos x-\sin2x\sin x=\frac{1}{\sqrt2};\\ \cos(2x+x)=\frac{1}{\sqrt2};\\ \cos3x=\frac{1}{\sqrt2};\\ 3x=\pm\arccos\frac{1}{\sqrt2}+2\pi n, n\in Z;\\ 3x=\pm\frac\pi4+2\pi n, n\in Z;\\ x=\pm\frac\pi{12}+\frac{2\pi n}{3}, n\in Z;$