Question

Доказать тождество sina+tga/1+cosa= tga

Answer 1

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