Question

(1-sinа)/(cosа)-(cosа)/(1+sinа) упросите

Answer 1

$\displaystyle\bf\\\frac{1-Sin\alpha }{Cos\alpha } -\frac{Cos\alpha }{1+Sin\alpha } =\frac{(1-Sin\alpha )\cdot(1+Sin\alpha )-Cos\alpha \cdot Cos\alpha }{Cos\alpha \cdot(1+Sin\alpha )} =\\\\\\=\frac{(1-Sin^{2} \alpha) -Cos^{2}\alpha }{Cos\alpha (1+Sin\alpha )} =\frac{Cos^{2}\alpha -Cos^{2} \alpha }{Cos\alpha (1+Sin\alpha )} =0$