Question

Solve $\frac{\cos x-\cos 2x}{1-\cos x}$

Answer 1

$\frac{\cos x-\cos 2x}{1-\cos x}$

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

$=\frac{\cos x-{\cos }^{2}x+(1-{\cos }^{2}x)}{1-\cos x}$

$=\frac{\cos x(1-\cos x)+(1-\cos x)(1+\cos x)}{1-\cos x}$

$=\cos x+(1+\cos x)=2cosx+1$