Question

Упростите выражение

Answer 1

$1) 1-2sin^2alpha+cos(4alpha-2pi)=cos2alpha+cos(2pi-4alpha)=2cosfrac{2alpha+2pi-4alpha}{2}cos frac{2alpha-2pi+4alpha}{2}=2cos(pi-alpha)cos(pi-3alpha)=2cosalphacos3alpha.$

$2) sin(frac{pi}{3}+alpha) +sin(frac{pi}{3}-alpha)=2sinfrac{frac{pi}{3}+alpha+frac{pi}{3}-alpha}{2}cos frac{frac{pi}{3}+alpha-frac{pi}{3}+alpha}{2}=2sinfrac{pi}{3}cdotcosalpha=2cdotfrac{sqrt3}{2}cdotcosalpha=sqrt{3}cosalpha$