Q) Prove that: $\frac{\sin\theta}{1 + \cos\theta} + \frac{1 + \cos\theta}{\sin\theta}$ = 2 cosec θ

LHS = $\frac{\sin\theta}{1 + \cos\theta} + \frac{1 + \cos\theta}{\sin\theta}$ = $\frac{\sin^2\theta + (1 + \cos\theta)^2}{\sin\theta (1 + \cos\theta)} $ = $\frac{\sin^2\theta + 1 + \cos^2\theta + 2\cos\theta}{\sin\theta (1 + \cos\theta)} $ = $\frac{1 + 1 + 2\cos\theta}{\sin\theta (1 + \cos\theta)} $ = $\frac{2 + 2\cos\theta}{\sin\theta (1 + \cos\theta)} $ = $\frac{2(1 + \cos\theta}{\sin\theta (1 + \cos\theta)} $ = $\frac{2}{\sin\theta}$ = 2 cosecθ = RHS ……… Hence Proved !