**Q) **If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B.

**Ans: **

Given that sin(A – B) = 0

Since we know that, sin 0^{0} = 0

A – B = 0 ……….. (i)

Also we are given that 2 cos (A + B) -1 = 0

or cos (A + B) =

Since we know that, cos 60^{0} =

A + B = 60 ……….. (ii)

By solving equations (i) and (ii), we get:

**A = 30 ^{0 }, B = 30^{0}**

*Check: both angle values are of acute angles, hence our answer is correct.*