NIMCET 2017 — Mathematics PYQ

Concept:
cos A - cos B = 2 sin ($\frac{B+A}{2}$) sin ($\frac{B-A}{2}$)

Calculations:
To express (cos 5x - cos 7x) as a product of sines or cosines or sines and cosines we know the trigonometric formula,
cos A - cos B = 2 sin ($\frac{B+A}{2}$) sin ($\frac{B-A}{2}$)
Here, A = 5x and B = 7x
(cos 5x - cos 7x) = 2 sin ($\frac{7x+5x}{2}$) sin ($\frac{7x-5x}{2}$)
(cos 5x - cos 7x) = 2 sin 6x sin x