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

Simplifying the expression: \[\n\frac{\sqrt{1 + \sin x}}{1 - \sin x}\n\] Applying the identity \( \sec^2 x - \tan^2 x = 1 \), we get: \[\n\frac{\sqrt{1 + \sin x}}{1 - \sin x} = \sec x \cdot \tan x\n\] Therefore, the answer is \( \sec x \cdot \tan x \).