Pythagorean identities for JEE

Formula

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

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

Conditions: Second and third identities where defined.

Most trigonometric simplifications, equation solving, and substitutions.