Question

Demonstre a seguinte identidade:
sec²x . cossec²x= sec²x + cossec²x

Answer 1

$sec^2x.cossec^2x=sec^2x+cossec^2x\\ \\ \frac{1}{cos^2x}.\frac{1}{sen^2x}=\frac{1}{cos^2x}+\frac{1}{sen^2x}\\ \\ \frac{1}{sen^2xcos^2x}=\frac{sen^2x+cos^2x}{sen^2xcos^2x}\\ \\ \frac{1}{sen^2xcos^2x}=\frac{1}{sen^2xcos^2x}$