Question: Prove that: \dfrac{1 + cos \alpha}{sin \alpha} = cot \frac{\alpha}{2}

Solution:

Taking LHS

= \dfrac{1 + cos \alpha}{sin \alpha}

$= \dfrac{(sin^2 \frac{\alpha}{2} + cos^2\frac{\alpha}{2}) + (cos^2 \frac{\alpha}{2} - sin^2 \frac{\alpha}{2})}{sin \alpha}$

= \dfrac{2cos^2 \frac{\alpha}{2}}{2 sin \frac{alpha}{2} cos \frac{\alpha}{2}}

= \dfrac{cos \frac{\alpha}{2}}{sin \frac{\alpha}{2}}

= cot \frac{alpha}{2}

RHS

#proved