Simplify:  $$\frac{ sin⁡A}{1+cos⁡A}+\frac{1+cos⁡A}{sin⁡A}$$​.

Correct option is D

Given: 

​$$\frac{ sin⁡A}{1+cos⁡A}+\frac{1+cos⁡A}{sin⁡A}$$​.

Formula Used:

​$$\sin^2 A + \cos^2 A = 1 \\ \implies \sin^2 A = 1 - \cos^2 A$$​​

Explanation:

$$\frac{\sin A}{1+\cos A} + \frac{1+\cos A}{\sin A} \\ \ \\ \Rightarrow \frac{\sin^2 A + (1+\cos A)^2}{\sin A (1+\cos A)} \\ \ \\ \Rightarrow \frac{1-\cos^2 A + (1+\cos A)^2}{\sin A (1+\cos A)}\\ \ \\ \Rightarrow \frac{(1+\cos A)(1-\cos A) + (1+\cos A)^2}{\sin A (1+\cos A)}\\ \ \\ \Rightarrow \frac{(1+\cos A) [1-\cos A + 1+\cos A]}{\sin A (1+\cos A)}\\ \ \\ \Rightarrow \frac{2}{\sin A}\\ \ \\\Rightarrow \bf 2 \cosec A$$