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  4. ∫ ( cos 2 x- cos 2 θ/ cos x- cos θ) d x is equal to

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Q. $\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x$ is equal to

Integrals

Solution:

$\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d \theta$
$=\int \frac{2 \cos ^{2} x-1-\left(2 \cos ^{2} \theta-1\right)}{\cos x-\cos \theta} d \theta$
$=2 \int \frac{\cos ^{2} x-\cos ^{2} \theta}{\cos x-\cos \theta} d \theta$
$=2 \int(\cos x+\cos \theta) d \theta$
$=2 \sin x+2 x \cos \theta+C$