# The expression √(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ) is equal to :

- 2 sec θ
- 2 tan θ
- 2 (1-sin θ)/cos θ
- 2 sin θ

**Answer: (1) 2 secθ**

**Explanation:-**

√(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ)

= √(1 + sinθ) (1 + sinθ)/(1 – sinθ)(1 + sinθ) + √(1-sinθ) (1- sinθ)/(1+ sinθ)(1-sinθ)

= √[(1 + sinθ)²/1 – sin²θ] + √[(1- sinθ)²/1 – sin²θ]

= √[(1 + sinθ)²/cos²θ] + [(1- sinθ)²/cos²θ]

= (1 + sinθ)/cosθ + (1- sinθ)/cosθ

= (1 + sinθ + 1- sinθ)/cosθ

= 2/cosθ

= 2 secθ

Then, the value of √(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ) is equal to 2 secθ.

Hence, the correct answer is option (1) 2 secθ.