Question

Sin a. 1+ cos a
------------. + --------------
1 + cos a. Sin a
Спростіть вираз

Answer 1

$\frac{Sin\alpha}{1+Cos\alpha}+\frac{1+Cos\alpha}{Sin\alpha}=\frac{Sin^{2}\alpha+1+2Cos\alpha+Cos^{2}\alpha}{Sin\alpha(1+Cos\alpha)}=\frac{2+2Cos\alpha}{Sin\alpha(1+Cos\alpha)}=\frac{2(1+Cos\alpha)}{Sin\alpha(1+Cos\alpha)}=\frac{2}{Sin\alpha}=2Cosec\alpha$