Question

The value of \( \frac{\sqrt{1 + \sin x}}{1 - \sin x} \) is:

• A. \( \tan x - \sec x \)
• B. \( \sec x - \tan x \)
• C. \( \sec x \cdot \tan x \)
• D. \( \sec x + \tan x \)

Hint:

In trigonometric expressions, try to apply standard identities to simplify the terms wherever possible.

Answer 1

The Correct Option is C

We simplify the given expression: \[ \frac{\sqrt{1 + \sin x}}{1 - \sin x} \] Using the identity \( \sec^2 x - \tan^2 x = 1 \), we can rewrite the expression as: \[ \frac{\sqrt{1 + \sin x}}{1 - \sin x} = \sec x \cdot \tan x \] Thus, the correct answer is \( \sec x \cdot \tan x \).