# JEE Main & Advanced Mathematics Trigonometrical Ratios and Identities Formulae to Rransform The Product Into Sum or Difference

## Formulae to Rransform The Product Into Sum or Difference

Category : JEE Main & Advanced

(1) $2\sin A\cos B=\sin (A+B)+\sin (A-B)$

(2) $2\cos A\sin B=\sin (A+B)-\sin (A-B)$

(3) $2\cos A\cos B=\cos (A+B)+\cos (A-B)$

(4) $2\sin A\sin B=\cos (A-B)-\cos (A+B)$

Let $A+B=C$ and $A-B=D$

Then, $A=\frac{C+D}{2}$ and $B=\frac{C-D}{2}$

Therefore, we find out the formulae to transform the sum or difference into product.

(1) $\sin C+\sin D=2\sin \frac{C+D}{2}\cos \frac{C-D}{2}$

(2) $\sin C-\sin D=2\cos \frac{C+D}{2}\sin \frac{C-D}{2}$

(3) $\cos C+\cos D=2\cos \frac{C+D}{2}\cos \frac{C-D}{2}$

(4) $\cos C-\cos D=2\sin \frac{C+D}{2}\sin \frac{D-C}{2}=-2\sin \frac{C+D}{2}\sin \frac{C-D}{2}$.

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