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 0⁰ = 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 60⁰ =

            A + B = 60 ……….. (ii)

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

A = 30⁰ , B = 30⁰

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