Question

Докажите тождество:​

Answer 1

$\frac{sin(\alpha-\pi )*cos(\alpha-2\pi )*sin(2\pi -\alpha)}{sin(90^{0} -\alpha )*ctg(180^{0} -\alpha )*ctg(270^{0} +\alpha )} =\frac{-sin\alpha*cos\alpha*(-sin\alpha )}{cos\alpha*(-ctg\alpha )*(-tg\alpha)} =sin^{2}\alpha$

cos α сокращается;

(-ctg α) * (-tg α) = 1

(-sin α) * (-sin α) = sin²α