Question

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

Answer 1

$cos2xcos x-sin2xsin x=frac{1}{sqrt2};\ cos(2x+x)=frac{1}{sqrt2};\ cos3x=frac{1}{sqrt2};\ 3x=pmarccosfrac{1}{sqrt2}+2pi n, nin Z;\ 3x=pmfracpi4+2pi n, nin Z;\ x=pmfracpi{12}+frac{2pi n}{3}, nin Z;$