Question

Give an expression of $\cos \theta$ in terms of $\text{cosec}\theta$.

Answer 1

$\cos \theta =\sqrt{1-{\sin }^2\theta }$

$=\sqrt{1-\frac{1}{{\csc }^2\theta }}$

$=\frac{\sqrt{{\csc }^2\theta -1}}{\csc \theta }$