Question

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

Answer 1

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