Question

Даю 30 балов , срочно надо ))))))))​

Answer 1

A

$\sin( - \frac{\pi}{4} ) - 3 \cos( \frac{\pi}{4} ) - tg( \frac{\pi}{6} ) + ctg( \frac{2\pi}{3} ) = \\ = - \frac{ \sqrt{2} }{2} - 3 \times \frac{ \sqrt{2} }{2} - \frac{ \sqrt{3} }{3} - \frac{ \sqrt{3} }{3} = \\ = - 4 \times \frac{ \sqrt{2} }{2} - \frac{2 \sqrt{3} }{3} = - 2 \sqrt{2} - \frac{2 \sqrt{3} }{3}$

Б

$\cos(18^{\circ}) \cos(63^{\circ}) + \sin(18^{\circ}) \sin(63^{\circ}) = \\ = \cos(18^{\circ} - 63^{\circ}) = \cos(45^{\circ}) = \frac{ \sqrt{2} }{2}$

В

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

Г

$\cos( \alpha - \beta ) - \cos( \alpha + \beta ) = \\ = \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) - ( \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) ) = \\ = \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) - \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) = \\ = 2 \sin( \alpha ) \sin( \beta )$