If p= sin Aover1+cos A , then sin Aover1-cos A is equal to:

If p= $sin A\over1+cos A$ , then $sin A\over1-cos A$ is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $1\over p$ .

p = sin A/(1 + cos A)

⇒ p = [sin A(1 + cos A)]/[(1 - cos A)(1 + cos A)]

⇒ p = [sin A(1 + cos A)]/(1 - cos²A)

⇒ p = [sin A(1 + cos A)]/sin²A [∵ 1 - cos²A = sin²A]

⇒ p = (1 + cos A)/sin A

⇒ 1/p = (1 + cos A)/sin A

Therefore, the value of the given expression is 1/p.

SSC CGL 2024 PYQ — Question 68