Question

помогите, срочно!
$\sqrt{( \cot {}^{2} a - \tan{}^{2}a ) \times cos2a } \times \tan(2a)$
спростить выражение если :
$\frac{\pi}{4} < a < \frac{\pi}{2}$
​

Answer 1

$\sqrt{(Ctg^{2}\alpha-tg^{2}\alpha)*Cos2\alpha}*tg2\alpha=\sqrt{\frac{1}{Sin^{2}\alpha}-1-\frac{1}{Cos^{2}\alpha}+1)*Cos2\alpha} *tg2\alpha =\sqrt{\frac{Cos^{2}\alpha-Sin^{2}\alpha}{Sin^{2}\alpha*Cos^{2}\alpha}*Cos2\alpha} *tg2\alpha=$

=$\sqrt{\frac{Cos^{2}2\alpha}{Sin^{2}\alpha*Cos^{2}\alpha}}*tg2\alpha=\frac{-Cos2\alpha}{Sin\alpha Cos\alpha}*\frac{Sin2\alpha}{Cos2\alpha}=-\frac{2Sin2\alpha}{2Sin\alpha Cos\alpha}=-\frac{2Sin2\alpha}{Sin2\alpha}=-2$

Answer 2

Ответ:  во вложении Объяснение: