Question

докажите тождества №5

Answer 1

$\frac{Cos^{2}\alpha-Cos^{2}\alpha Sin^{2}\beta}{Sin^{2}\alpha Sin^{2}\beta}=\frac{Cos^{2}\alpha(1-Sin^{2}\beta)}{Sin^{2}\alpha Sin^{2}\beta}=\frac{Cos^{2}\alpha Cos^{2}\beta}{Sin^{2}\alpha Sin^{2}\beta}=\frac{Cos^{2}\alpha}{Sin^{2}\alpha}*\frac{Cos^{2}\beta}{Sin\beta ^{2}}=Ctg^{2}\alpha Ctg^{2}\beta\\\\Ctg^{2}\alpha Ctg^{2}\beta=Ctg^{2}\alpha Ctg^{2}\beta$