Question

Докажите тождество:
2cos2x-1 sin3x-sinx 1
------------- + ---------------- = -------
2sinxcosx cos3x+cosx sin2x​

Answer 1

$frac{2cos^2x-1}{2, sinx, cosx}+frac{sin3x-sinx}{cos3x+cosx}=frac{cos2x}{sin2x}+frac{2sinxcdot cos2x}{2, cos2xcdot cosx}=frac{cos2x}{sin2x}+frac{sinx}{cosx}=\\=frac{cos2xcdot cosx+sinxcdot sin2x}{sin2xcdot cosx}=frac{cos(2x-x)}{sin2xcdot cosx}=frac{cosx}{sin2xcdot cosx}=frac{1}{sin2x}\\\frac{1}{sin2x}=frac{1}{sin2x}\\\star ; ; ; cos(alpha -beta )=cosalpha cdot cosbeta +sinalpha cdot sinbeta$