Mark the correct alternative in each of the following:
Question:

Mark the correct alternative in each of the following:

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

A. $2(\sin x+x \cos \theta)+C$

B. $2(\sin x-x \cos \theta)+C$

C. $2(\sin x+2 x \cos \theta)+C$

D. $2(\sin x-2 x \cos \theta)+C$

Solution:

$I=\int \frac{\left\{2(\cos x)^{2}-1\right)-\left[2(\cos \theta)^{2}-1\right]}{\cos x-\cos \theta} \mathrm{d}_{x}$

$I=2 \int \frac{(\cos x)^{2}-(\cos \theta)^{2}}{\cos x-\cos \theta} d x$

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

$I=2 \int(\cos x+\cos \theta) d x$

$I=2(\sin x+x \cos \theta)+c$

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