Express one ratio in terms of another for JEE

Formula

\(\sin^2 x=1-\cos^2 x,\quad \cos^2 x=1-\sin^2 x,\quad \tan^2 x=\sec^2 x-1,\quad \cot^2 x=\csc^2 x-1\)

Variables: \(x\in\mathbb{R}\).

Conditions: Where defined.

Identity manipulation and reducing expressions.