Question

If\[\int \frac{\sin^{\frac{2}{3}} x + \cos^{\frac{2}{3}} x}{\sqrt{\sin^{\frac{1}{3}} x \cos^{\frac{1}{3}} x \sin(x - \theta)}} \, dx = A \sqrt{\cos \theta \tan x - \sin \theta} + B \sqrt{\cos \theta \cot x + \sin(x - \theta)} + C,\]where \( C \) is the integration constant, then \( AB \) is equal to ______.

• A. \( 4 \csc(2\theta) \)
• B. \( 4 \sec \theta \)
• C. \( 2 \sec \theta \)
• D. \( 8 \csc(2\theta) \)

Answer 1

The Correct Option is D

The Correct Answer is