Question

sinxcos6x-cosxsin6x=√2/2

Answer 1

                                         $sin xcos 6x-cos xsin6x= frac{1}{ sqrt{2} } \ \ sin(x-6x)=frac{1}{ sqrt{2} } \ sin5x=-frac{1}{ sqrt{2} } \ \ 5x=(-1)^{k+1}cdot frac{pi}{4}+ pi k,k in mathbb{Z}\ \ boxed{x=(-1)^{k+1}cdot frac{pi}{20}+ frac{pi k}{5},k in mathbb{Z} }$