Lembre-se:
cossec x = 1/ sen x
sec x = 1 / cos x
tan x = sen x / cos x
Agora vamos lá:
[tex]A=\frac{cossec^2 x. tan x}{sec^2 x}=\frac{\frac{1}{sen^2x} \cdot \frac{senx}{cos x}}{\frac{1}{cos^2 x}}= \\ \\ A=\frac{\frac{1}{senx.cosx}}{\frac{1}{cos^2x}}=\frac{1}{senx.cosx}\cdot \frac{cos^2 x}{1}=\frac{cosx}{senx}=\boxed{cotang \ \ x}[/tex]
