Question

Evaluate \[ \int_{ \frac{\pi}{4} }^{ \frac{3\pi}{4} } \frac{1}{1 + \cos x} \, dx \]

• A. 2
• B. \( \frac{1}{2} \)
• C. \( \frac{1}{\sqrt{2}} \)
• D. \( -\frac{1}{2} \)

Hint:

Use trigonometric identities to simplify integrals involving cosine functions.

Answer 1

The Correct Option is A

Step 1: Use a trigonometric identity.
We use the identity \( 1 + \cos x = 2 \cos^2 \left( \frac{x}{2} \right) \) to simplify the integral.
Step 2: Conclusion.
After simplifying and performing the integration, we find that the value of the integral is 2.
Final Answer: \[ \boxed{2} \]