Question

sin^2a+ctg^2a+cos^2a=1/sin^2a

Answer 1

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