Question

Упростите выражение: (tg^2a-1)*cos^3(-a) / sin(0,5П+2a)

Answer 1

$frac{(tg^2a-1)*cos^3(-a)}{sin(0,5 pi +2a)} = -frac{(tg^2a-1)*cos^3a}{cos 2a} = frac{cos^3a-tg^2a*cos^3a}{cos 2a} = \ = frac{cos^3a-sin^2a*cos a}{cos 2a} = frac{cos a(cos^2a-sin^2a)}{cos 2a} = frac{cos a*cos 2a}{cos 2a}= cos a$