Question

Доказать тождество:
(cosa+tga)/(ctga+seca) = sina

Answer 1

$\frac{Cos\alpha+tg\alpha }{Ctg\alpha+Sec\alpha}= \frac{Cos\alpha+\frac{Sin\alpha }{Cos\alpha}}{\frac{Cos\alpha }{Sin\alpha}+\frac{1}{Cos\alpha}}=\frac{Cos^{2}\alpha+Sin\alpha}{Cos\alpha}:\frac{Cos^{2}\alpha+Sin\alpha}{Sin\alpha Cos\alpha} =\\\\=\frac{Cos^{2}\alpha+Sin\alpha}{Cos\alpha} *\frac{Sin\alpha Cos\alpha}{Cos^{2}\alpha+Sin\alpha}=Sin\alpha\\\\\boxed{Sin\alpha=Sin\alpha}$