Question

Докажите тождество!!!
ПРОШУ ВАС РАСПИШИТЕ ПОДРОБНО !!!
$frac{sin ^{4} alpha -cos^{4} alpha }{(1-cos alpha )(1+cos alpha )}$

Answer 1

$frac{sin^4a-cos^4a}{(1-cosa)(1+cosa)} = frac{(sin^2a-cos^2a)(sin^2a+cos^2a)}{1-cos^2a}= frac{sin^2a-cos^2a}{sin^2a} =\\=-frac{cos2a}{sin^2a} \\ili\\ ...=frac{sin^2a-cos^2a}{sin^2a}= frac{sin^2a}{sin^2a} - frac{cos^2a}{sin^2a}=1-ctg^2a$