Show that cos2x / (cosx - sinx) = cosx + sinx

cos2x / (cosx - sinx) = cosx + sinx 

Note that cos 2x  =  cos^2x  - sin^2 x....= (cos x - sin x) (cos x + sinx ).....so we have

(cos^2x - sin^2x )  / ( cosx - sin x)

(cosx + sin x) (cos x - sin x)  / (cos x - sin x )        divide out the  (cosx - sinx)

cos x + sin x  =    the right hand side

Thank you so much! Didnt think of the (a+b)*(a-b) rule!