# Express Each of the Following as the Product of Sines and Cosines: Cos 12x - Cos 4x - Mathematics

Sum

Express each of the following as the product of sines and cosines:
cos 12x - cos 4x

#### Solution

$\cos 12x - \cos 4x$
$= - 2\sin \left( \frac{12x + 4x}{2} \right) \sin \left( \frac{12x - 4x}{2} \right) \left\{ \because \cos A - \cos B = - 2\sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right) \right\}$
$= - 2 \sin 8x \sin 4x$

Concept: Transformation Formulae
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 8 Transformation formulae
Exercise 8.2 | Q 1.4 | Page 17