Question

Which of the following shows the simplified form of sine of x over the quantity 1 minus cosine of x end quantity question mark 1 sin x + tan x sin x + cot x csc x + cot x

Answer 1

Given:

$\frac{\sin x}{1-\cos x}$$\begin{gathered} \frac{\sin x}{1-\cos x}=\frac{\sin x}{1-\cos x}\times\frac{1+\cos x}{1+\cos x} \\ =\frac{\sin x+\text{sinx cosx}}{1-cos^2x} \\ =\frac{\sin x+\text{sinx cosx}}{\sin ^2x} \\ =\frac{1}{\sin x}+\frac{\cos x}{\sin x} \\ =\csc x+\cot x \end{gathered}$