Trigonometric Identities — Maths STD 10 — Question

$\text{L.H.S.}=\frac{\sin\theta}{(1+\cos\theta)}+\frac{(1+\cos^2\theta)}{\sin\theta}$

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

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

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

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

$=\frac{1-\cos\theta+1+\cos\theta}{\sin\theta}$

$=\frac{2}{\sin\theta}$

$=2\text{cosec}\theta$

$=\text{R.H.S.}$