Question

Найдите sinα*cosα, если tgα+ctgα= -8.

Answer 1

$tg\alpha +Ctg\alpha=-8\\\\\frac{Sin\alpha}{Cos\alpha}+\frac{Cos\alpha}{Sin\alpha}=-8\\\\\frac{Sin^{2}\alpha+Cos^{2}\alpha}{Sin\alpha*Cos\alpha}=-8\\\\\frac{1}{Sin\alpha*Cos\alpha}=-8\\\\Sin\alpha *Cos\alpha =-\frac{1}{8}\\\\Sin\alpha*Cos\alpha=-0,125\\\\Otvet:\boxed{Sin\alpha*Cos\alpha=-0,125}$