(1 + cos 'alpha')/sin 'alpha' = cot 'alpha'/2 | Prove | Trigonometry

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