Question

Докажите тождество
$frac{cosa-cos^3a}{sin^2a} =-sin( frac{3pi}{2} -a)$

Answer 1

$displaystyle frac{cos alpha-cos^3alpha }{sin^2alpha}= frac{cosalpha(1-cos^2alpha)}{sin^2alpha} = frac{cosalphasin^2alpha}{sin^2alpha} =cosalpha=-sinbigg( frac{3 pi }{2}-alphabigg)$