Indefinite Integration
Trigonometric Integration
Grade 12
Question:
<p>\(\int \frac{\cos 2x - \cos 2a}{\cos x - \cos a} dx\) is equal to</p>
<p>(a) \(2 \sin x + 2x \cos a + C\)</p>
<p>(b) \(\sin x + x \cos a + C\)</p>
<p>(c) \(2\sin x + x \cos x + C\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use trigonometric identities for difference of cosines to simplify the integrand before integration.
<p><strong>Solution:</strong> Using the identity $\cos 2x - \cos 2a = -2\sin(x+a)\sin(x-a)$ and $\cos x - \cos a = -2\sin\frac{x+a}{2}\sin\frac{x-a}{2}$, we can simplify the integrand and integrate to get $2\sin x + 2x\cos a + C$.</p>
Correct Answer: A