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Express (cos 5x - cos 7x) as a product of sines or cosines.1. 2 cos 4x cos x2. 2 sin 4x sin x3. 2 sin 6x sin x4. 2 cos 6x cos x

Answer» Correct Answer - Option 3 : 2 sin 6x sin x

Concept:

cos A - cos B = 2 sin \(\rm (\frac {B + A}{2})\) sin \(\rm (\frac {B - A}{2})\) 

 

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 \(\rm (\frac {B + A}{2})\) sin \(\rm (\frac {B - A}{2})\) 

Here, A = 5x and B = 7x 

(cos 5x - cos 7x) = 2 sin \(\rm (\frac {7x + 5x}{2})\) sin \(\rm (\frac {7x - 5x}{2})\) 

(cos 5x - cos 7x) = 2 sin 6x sin x



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