Question

Simplify $\frac{\cos 2x-\cos 2\alpha }{\cos x-\cos \alpha }$

Answer 1

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

$=\frac{2{\cos }^{2}x-1-2{\cos }^2\alpha +1}{cosx-cos\alpha }$

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

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

$=\frac{2(\cos x+\cos \alpha )(cosx-cos\alpha )}{(cosx-cos\alpha )}$

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