Question

A expressão sec x - cos x
_______________
cossec x - sen x
é equivalente a :

Answer 1

 Saiba que, $\sin^2x+\cos^2x=1$


$\frac{sec\,x-\cos\,x}{cossec\,x-\sin\,x}=\\\\\frac{\frac{1}{\cos\,x}-\cos\,x}{\frac{1}{\sin\,x}-\sin\,x}=\\\\\frac{1-\cos^2x}{\cos\,x}\div\frac{1-\sin^2x}{\sin\,x}=\\\\\frac{\sin^2x}{\cos\x}\times\frac{\sin\,x}{\cos^2x}=\\\\\frac{\sin^3x}{\cos^3x}=\\\\\boxed{\left(\frac{\sin\,x}{\cos\,x}\right)^3}$