Indefinite Integration
Trigonometric Functions
Grade 12
Question:
<p>Evaluate \(\int \frac{1}{\cos x} \cdot \sin 2x \cdot \cos 2x \, dx\)</p>
<p>(A) \(\frac{2}{10}(1-\cos x)^{2}(3-2\cos x)^{3/2} + C\)</p>
<p>(B) \(\frac{2}{5}(1-\cos x)^{2}(3-2\cos x)^{3/2} + C\)</p>
<p>(C) \(\frac{2}{5}(1-\cos x)^{2}(3-2\cos x)^{3/2} + C\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Use trigonometric identities and substitution to simplify the integrand before integration.
<p>This is an indefinite integral problem requiring trigonometric substitution and algebraic manipulation.</p>
Correct Answer: B