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CBSE Class 12 · 2007 · Indefinite IntegralsVery Short Answer

Evaluate :

\int cos 4 x cos 3 x d x

Answer: $\frac{1}{14} sin 7 x + \frac{1}{2} sin x + C$

Solution

Convert the product to a sum using

2 cos A cos B = cos (A + B) + cos (A - B)

:

cos 4 x cos 3 x = \frac{1}{2} (cos 7 x + cos x) .

Integrating,

\frac{1}{2} \int (cos 7 x + cos x) d x = \frac{1}{14} sin 7 x + \frac{1}{2} sin x + C

CBSE Class 12 Board · 2007 · Subjective

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