Question

Cscθ - sinθ = _____

Answer 1

So you maybe know that $\csc x = \frac{1}{\sin x}$. Now let us try to simplify the expression

$\csc x - \sin x = \frac{1}{\sin x} - \sin x = \frac{1}{\sin x} - \frac{\sin^2 x }{\sin x}=\frac{1-\sin^2 x}{\sin x} =$

$= \frac{\cos^2 x}{\sin x} = \cot x \cdot \cos x$