Question

$1. sin(x + frac{2pi}{3} ) * sin(x - frac{pi}{3}) 2. sin(x + frac{pi}{4} ) * sin(x - frac{pi}{3})$

Answer 1

$sin(x + frac{2pi}{3} ) sin(x - frac{pi}{3}) = \ =0,5(cos(x + frac{2pi}{3}-x+ frac{pi}{3})-cos(x + frac{2pi}{3}+x - frac{pi}{3}))= \ =0,5(cospi-cos(2x + frac{pi}{3} ))=-0.5-0.5cos(2x + frac{pi}{3} )$

$sin(x + frac{pi}{4} ) sin(x - frac{pi}{3}) = \ =0,5(cos(x + frac{pi}{4}-x+ frac{pi}{3})-cos(x + frac{pi}{4}+x - frac{pi}{3}))= \ =0,5(cos frac{7pi}{12}-cos(2x- frac{pi}{12}))= 0,5cos frac{7pi}{12}-0.5cos(2x- frac{pi}{12})$