If 2cosAcosB=cos(x)+cos(y)2cosAcosB=cos(x)+cos(y), then x+y=x+y=??

1 Answer
Sep 16, 2016

2A

Explanation:

cos x + cos y = 2cos A.cos B (1)
Use trig identity:
cos x + cos y = 2cos ((x + y)/2).cos ((x - y)/2)cosx+cosy=2cos(x+y2).cos(xy2)(2)
Compare (1) and (2), we get:
A = (x + y)/2A=x+y2
(x + y) = 2A(x+y)=2A