Question

Prove that $\frac{sinx}{1-cosx}=cosecx+cotx$

Answer 1

$\frac{\sin x}{1-\cos x}=cosecx+\cot x$

solving LHS we get

$\frac{\sin x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x}$

$\Rightarrow \frac{\sin x(1+\cos x)}{1-{\cos }^{2}x}$

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

$\Rightarrow cosecx+\cot x=$RHS

Proved.