JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int\left(\frac{\sin \theta}{\cos 3 \theta}+\frac{\sin 3 \theta}{\cos 9 \theta}+\frac{\sin 9 \theta}{\cos 27 \theta}\right) d \theta

is equal to

View answer and explanation

Correct option: C

\frac{1}{2} \log \left|\frac{\sqrt[27]{\sec 27 \theta}}{\sec \theta}\right|+C

Option D (None of these) is incorrect. Option C (

\frac{1}{2} \log \left|\frac{\sqrt[27]{{\sec 27 \theta}}}{{\sec \theta}}\right|+C

) is the correct answer, obtained by using trigonometric identities to simplify the integral.

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