Question

(csc^(2)ϕ)/(1+tan^(2)ϕ)=cot^(2)ϕ

Answer 1

Hola.

$\frac{csc^{2}(\alpha)}{1+tan^{2}(\alpha)}=cot^{2}(\alpha)$

$\frac{\frac{1}{sen^{2}(\alpha)}}{1+\frac{sen^{2}(\alpha)}{cos^{2}(\alpha)}}=cot^{2}(\alpha)$

$\frac{\frac{1}{sen^{2}(\alpha)}}{\frac{cos^{2}(\alpha)+sen^{2}(\alpha)}{cosx^{2}(\alpha)}} =cot^{2}(\alpha)$

$\frac{\frac{1}{sen^{2}(\alpha)}}{\frac{1}{cos^{2}(\alpha)}}=cot^{2}(\alpha)$

$\frac{1}{senx^{2}(\alpha )}: \frac{1}{cos^{2}(\alpha)} = cot^{2}(\alpha)$

$\frac{1}{sen^{2}(\alpha)} *\frac{cos^{2}(\alpha)}{1} =cot^{2}(\alpha)$

$\frac{cos^{2}(\alpha)}{sen^{2}(\alpha)} =cot^{2}(\alpha)$

$cot^{2}(\alpha)=cot^{2}(\alpha)$  //

Identidades

csc² = 1 / sen²

tan² = sen² / cos²

sen² + cos² = 1

cot² = cos² / sen²

Un cordial saludo.