Question

упростите выражение: cosa+ctga/1+sina

Answer 1

$\frac{Cos\alpha+Ctg\alpha}{1+Sin\alpha}=\frac{Cos\alpha+\frac{Cos\alpha}{Sin\alpha}}{1+Sin\alpha }=\frac{\frac{Sin\alpha Cos\alpha+Cos\alpha}{Sin\alpha}}{1+Sin\alpha}= \frac{Cos\alpha(Sin\alpha+1)}{Sin\alpha(1+Sin\alpha)}=\frac{Cos\alpha }{Sin\alpha }=Ctg\alpha$