Question

Evaluate : $\int \frac{cos2x-cos2\alpha }{cosx-cos\alpha }dx$

Answer 1

$\int \frac{\cos 2x-\cos 2\alpha }{\cos x-\cos \alpha }dx$

$=\int \frac{(2{\cos }^{2}x-1)-(2{\cos }^2\alpha -1)}{\cos x-\cos \alpha }dx$

$=2\int \frac{({\cos }^{2}x-{\cos }^2\alpha )}{\cos x-\cos \alpha }dx$

$=2\int \cos x+\cos \alpha dx$

$=2[\int \cos xdx+\cos \alpha \int dx]$

$=2[\sin x+x\cos \alpha ]+c$