Question

Доказать тождство:
sin(-a)+cos(п+a)/1+2cos(п/2-a)cos(-a)

Answer 1

$\frac{ \sin( - a) + \cos(\pi + a) }{1 + 2 \cos( \frac{\pi}{2} - a ) \cos( - a) } = \frac{ - \sin(a) + \cos( - a) }{1 + 2 \sin(a) \cos( - a) } = \frac{ - \sin(a) + \cos(a) }{ { \sin(a) }^{2} + { \cos(a) }^{2} + 2 \sin(a) \cos(a) } = \frac{ - \sin(a) + \cos(a) }{( \sin(a)+ \cos(a) ){}^{2} } = - 1$