Question

cos^2(п-а)/tg^2(a-3п/2)+sin^2(2п-а)/tg^2(a-п/2)

Answer 1

Ответ:

$\frac{ { \cos}^{2} (\pi - \alpha )}{ {tg}^{2} ( \alpha - \frac{3\pi}{2} )} + \frac{ { \sin}^{2}(2\pi - \alpha ) }{ {tg}^{2} ( \alpha - \frac{\pi}{2}) } = \\ = \frac{ { \cos}^{2} ( \alpha )}{ {ctg}^{2} ( \alpha )} + \frac{ { \sin }^{2}( \alpha )}{ {ctg}^{2} ( \alpha )} = \frac{ { \cos}^{2}( \alpha ) + { \sin }^{2} ( \alpha )}{ {ctg}^{2}( \alpha ) } = \\ = \frac{1}{ {ctg}^{2} ( \alpha )} = {tg}^{2} ( \alpha )$