Question

Упросите выражение: ( sin⁡(π-α) ·ctg(3π/2-α))/( tg(2π-α)cos(π/2+α))-cos^2 α

Answer 1

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