cos 2 x - cos 2 cos x - cos d x is equal to:

Question

$\int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} d x$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. $2 (s i n x + x c o s θ) + C$

Explanation:

Let $I = \int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} d x$

$= \int \frac{(2 \cos^{2} x - 1) - (2 \cos^{2} θ - 1)}{\cos x - \cos θ} d x$

$= 2 \int \frac{\cos^{2} x - \cos^{2} θ}{\cos x - \cos θ} d x$

$= 2 \int \frac{(\cos x - \cos θ) (\cos x + \cos θ)}{\cos x - \cos θ} d x$

$= 2 \int (\cos x + \cos θ) d x$

$= 2 (\sin x + x \cos θ) + C$

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