Math problem sin 2x = -cos(x-10)

sin 2x = -cos(x-10) => sin 2x + cos(x-10) = 0 => sin 2x + sin(pi/2 - (x-10)) = 0 (here the reduction formulas were used), then use the formulas of sum transformation into the product.

Edited, since I commited mistake. Sorry for that.