# What is [(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)] equal to ?

What is [(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)] equal to ?

- Sec A – tan A
- 2 sec A . tan A
- 4 sec A. tan A
- 4 cosec A . cot A

**Answer: (3) 4 sec A. tan A**

**Explanation:-**

[(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)]

= [(1 + sin A) (1 + sin A)/(1 – sin A) (1 + sin A)] – [(1 – sin A) (1 – sin A)/(1 + sin A) (1 – sin A)]

=[1 + sin^{2} A + 2 sin A)/(1 – sin^{2} A) – (1 + sin^{2} A – 2 sin A)/(1 – sin^{2} A)

=(1 + sin^{2} A + 2 sin A – 1 – sin^{2}A + 2 sin A)/ (1 – sin^{2}A)

= (2 sin A + 2sinA )/cos^{2}A

= 4sin A/cos^{2}A

= 4 sin A/cos A x cos A

= 4 sec A tan A.

Hence, the answer is (3) 4 sec A. tan A.