Question

The value of the integral \( \int_0^{\frac{\pi}{2}} \log (\tan x) \, dx \) is:

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

Hint:

Use symmetry in integrals to simplify calculations, especially for integrals involving \( \tan x \) and \( \cot x \).

Answer 1

The Correct Option is A

Step 1: Solve the integral. The integral \( \int_0^{\frac{\pi}{2}} \log (\tan x) \, dx \) evaluates to 0 due to the symmetry of the integrand.
Step 2: Conclusion. Thus, the value of the integral is 0.