Question

If $A+B+C=\pi$, then $\cos B+\cos C$ is equal to

• A. $2\cos \frac{A}{2}\cos \frac{B-C}{2}$
• B. $\sin \frac{A}{2}\cos \frac{B-C}{2}$
• C. $2\cos \frac{C}{2}\cos \frac{A-B}{2}$
• D. $2\cos \frac{B}{2}\cos \frac{C}{2}$

Answer 1

The correct option is A $2\cos \frac{A}{2}\cos \frac{B-C}{2}$

$\cos B+\cos C=2\cos \left(\frac{B+C}{2}\right)\cos \left(\frac{B-C}{2}\right)$

Now$A+B+C=$ $\pi$

$\therefore (\frac{B+C}{2}=\frac{\pi -A}{2})$

$\therefore \cos \left(\frac{B+C}{2}\right)=\left(\cos \frac{A}{2}\right)$

$\therefore \cos B+\cos C=2\cos \left(\frac{A}{2}\right)cos\left(\frac{B-C}{2}\right)$