What is the value of $$\sqrt\frac{1+\text{sin\space\text{A}}}{1-\text{sin}\space\text{A}}$$​ ?

Correct option is A

Given:​

​$$\sqrt\frac{1+\text{sin\space\text{A}}}{1-\text{sin}\space\text{A}}$$

Formula Used:

sin²A + cos²A = 1

$$\sec A=\frac 1{\cos A}$$ , tan A =$$\frac{\sin A}{\cos A}$$​​

Solution:

$$\sqrt\frac{1+\text{sin\space\text{A}}}{1-\text{sin}\space\text{A}}$$​​

=$$\sqrt{\frac{1+\text{sin\space\text{A}}}{1-\text{sin}\space\text{A}} \times\frac{1+\text{sin\space\text{A}}}{1+\text{sin}\space\text{A}} }$$

= $$\sqrt\frac{(1+\text{sin A})^2}{1-\sin^2 A}$$

= $$\frac{1+\text{sin\space\text{A}}}{\cos A}$$

= $$\frac 1{\cos A}+\frac{\sin A}{\cos A}$$

= sec A + tan A