Question

Evaluate the integral \[ \int \frac{dx}{\cos 2x - \cos^2 x} \]

• A. \( -\cot x + c \)
• B. \( \tan x + c \)
• C. \( -\tan x + c \)
• D. \( \cot x + c \)

Hint:

When dealing with trigonometric integrals, use identities to simplify the expression before integrating.

Answer 1

The Correct Option is D

Step 1: Use trigonometric identities.
We can use the identity \( \cos 2x = 2 \cos^2 x - 1 \) to simplify the integrand. Substituting this identity into the expression, we get a simpler integrand that can be integrated easily.

Step 2: Perform the integration.
After simplifying, we integrate the function and find that the result is \( \cot x + c \).

Step 3: Conclusion.
Thus, the correct answer is \( \cot x + c \), corresponding to option (D).