Question

The integral \[ \int_0^{\frac{\pi}{2}} \frac{1 - \cot x}{\csc x + \cos x} \, dx = \]

• A. 0
• B. \( \frac{\pi}{2} \)
• C. 1
• D. \( \frac{\pi}{4} \)

Hint:

Simplify the integrand using trigonometric identities before attempting to integrate.

Answer 1

The Correct Option is A

Step 1: Simplify the integrand.
The integral involves trigonometric functions, and we use trigonometric identities to simplify it. After simplifying, we integrate the expression.
Step 2: Conclusion.
Thus, the value of the integral is 0, corresponding to option (A).