Expression $$\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}$$​ is equal to:

Correct option is C

Given:
Expression: $$\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}$$​​
Formula Used:
​$$\sin^2\theta + \cos^2\theta = 1$$​​

​$$\sec\theta = \frac{1}{\cos\theta}$$​​

​$$\tan\theta = \frac{\sin\theta}{\cos\theta}$$​​
Solution:
Multiply the numerator and the denominator inside the square root by $$(1 + \sin\theta):$$​​
​$$= \sqrt{\frac{(1+\sin\theta)(1+\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}}$$​​

​$$= \sqrt{\frac{(1+\sin\theta)^2}{1-\sin^2\theta}}$$​​

Since $$1-\sin^2\theta = \cos^2\theta:$$​​

​$$= \sqrt{\frac{(1+\sin\theta)^2}{\cos^2\theta}}$$​​
Taking the square root:
​$$= \frac{1+\sin\theta}{\cos\theta}$$​​
Separate the terms:
​$$= \frac{1}{\cos\theta} + \frac{\sin\theta}{\cos\theta}$$​​
​$$= \sec\theta + \tan\theta$$​​
Final Answer
So the correct answer is (c)