Question

Prove that $\frac{1+cos\theta -si{n}^2\theta }{sin\theta (1+cos\theta )}=cot\theta$

Answer 1

$LHS=\frac{1+cos\theta -si{n}^2\theta }{sin\theta (1+cos\theta )}$

$=\frac{{\cos }^2\theta +\cos A}{\sin \theta (1+\cos \theta )}$

$=\frac{\cos \theta (1+\cos \theta )}{\sin A(1+\cos \theta )}$

$=\cot \theta$

$=RHS$

Hence proved