Question

1+tga/1+ctga если cos a=3/5 3п/2 2п

Answer 1

$\frac{1+tg\alpha}{1+Ctg\alpha }=\frac{1+tg\alpha}{1+\frac{1}{tg\alpha}}=\frac{1+tg\alpha}{\frac{tg\alpha+1}{tg\alpha}}=\frac{(1+tg\alpha)*tg\alpha}{tg\alpha+1}=tg\alpha\\\\\frac{3\pi }{2}<\alpha<2\pi \Rightarrow Sin\alpha<0\\\\Sin\alpha =-\sqrt{1-Cos^{2} \alpha}=-\sqrt{1-(\frac{3}{5} )^{2} } =-\sqrt{1-\frac{9}{25} }=-\sqrt{\frac{16}{25}}=-\frac{4}{5}\\\\tg\alpha=\frac{Sin\alpha }{Cos\alpha}=-\frac{4}{5}:\frac{3}{5}=-\frac{4}{5} *\frac{5}{3}=-\frac{4}{3}=-1\frac{1}{3}$

$Otvet:\boxed{-1\frac{1}{3}}$