Question

Evaluate $a$ if $\int \frac{\cos 2x-\cos 2\alpha }{\cos x-\cos \alpha }dx$=$a(\sin x+x\cos \alpha )$+$c$

Answer 1

We know $\cos 2\theta =2{\cos }^2\theta -1$

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

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

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

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

$=2(\sin x+x\cos \alpha )+c$