Q. Let $ \alpha ,\beta $ be such that $ \pi <\alpha -\beta <3\pi $ . If $ \sin \alpha +\sin \beta =-\frac{21}{65} $ and $ \cos \alpha +\cos \beta =-\frac{27}{65}, $ then the value of $ \cos \frac{\alpha -\beta }{2} $ is
JamiaJamia 2007
Solution: