Question

If $A+B=\frac{\pi }{3}$ and $cosA+cosB=1$ then find the value of $\cos \frac{(A-B)}{2}$

Answer 1

$\cos A+\cos B=1$

$2\cos \left[\frac{A+B}{1}\right].\cos \left[\frac{A-B}{2}\right]=1$

$2\cos \left[\frac{\pi }{6}\right]\cos \left[\frac{A-B}{2}\right]=1$

$\cos \left[\frac{A-B}{r}\right]=\frac{1}{\sqrt{3}}$