If $$\frac{\text{cos}\space{\text{A}}}{1-\text{sin}\space\text{A}}+\frac{\text{cos}\space{\text{A}}}{1+\text{sin}\space\text{A}}=4$$​, then what will be the value of A?

Correct option is B

Given:

​$$\frac{\cos A}{1 - \sin A} + \frac{\cos A}{1 + \sin A} = 4$$​​

Formula Used:
$$\sin^2 A + \cos^2 A = 1.$$​​

Solution:

​$$\frac{\cos A}{1 - \sin A} + \frac{\cos A}{1 + \sin A} = 4$$​​

​$$\cos A \left( \frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} \right) = 4$$​​

​$$\cos A \left( \frac{(1 + \sin A) + (1 - \sin A)}{1 - \sin^2 A} \right) = 4$$​​

​$$\cos A \left( \frac{2}{\cos^2 A} \right) = 4$$​​

​$$\frac{2}{\cos A} = 4$$​

cos A $$= \frac{1}{2}$$​

A = $$60^\circ$$​​