Question

Which of the following relations is incorrect?

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

Answer 1

The correct option is D

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

Relations $\left(1\right),\left(2\right)$ and $\left(3\right)$ are correct.

Whereaas $4^{th}$ relation can be written as

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