Expressions involving inverse cotangent for JEE

Formula

\(\sin(\cot^{-1}x)=\dfrac{1}{\sqrt{1+x^2}},\quad \cos(\cot^{-1}x)=\dfrac{x}{\sqrt{1+x^2}}\)

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

Conditions: Using principal range \((0,\pi)\); sign of cosine follows sign of \(x\).

Algebraic conversion of inverse cotangent expressions.