$\int\frac{\cos 2x- \cos 2a}{\cos x-\cos a}dx$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $2 \sin x + 2x \cos a +C$, where C is an arbitary constant
$\displaystyle \int \frac{\cos2x-\cos2a}{\cos x-\cos a}\,dx$
$\cos2x-\cos2a=2(\cos^2x-\cos^2a)=2(\cos x-\cos a)(\cos x+\cos a)$
$\displaystyle \int \frac{\cos2x-\cos2a}{\cos x-\cos a}\,dx=\int 2(\cos x+\cos a)\,dx$
$\displaystyle =2\sin x+2x\cos a+C$