Question

Докажите тождество :ctga/tga+ctga=cos^2a

Answer 1

$\frac{ctga}{tga+ctga} = \frac{ctga}{ \frac{sina}{cosa} + \frac{cosa}{sina} } = \frac{ctga}{ \frac{sin^2 a+ cos^2 a}{cosa *sina} } = \\ \\ = \frac{ \frac{cosa}{sina} }{ \frac{1}{cosa* sina} } = \frac{cosa}{sina}* cosa *sina = cos^2 a$