Question

$\int \frac{cos2x-cos2\theta }{cosx-cos\theta }dx$ is equal to

• A. $2(sinx+xcos\theta )+C$
• B. $2(sinx-xcos\theta )+C$
• C. $2(sinx+2xcos\theta )+C$
• D. $2(sinx-2xcos\theta )+C$

Answer 1

The correct option is A $2(sinx+xcos\theta )+C$

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