Question

If 2 cos (A + B) = 2 sin (A - B) = 1;
find the values of A and B.

Answer 1

2 cos (A + B) = 1

cos (A + B) = `(1)/(2)`

cos (A+B) = cos 60°
A + B = 60°            ........( 1)

2 sin (A – B) = 1

2 sin (A – B) = `(1)/(2)`

A – B = 30°             ........(2)
Adding (1) and (2)

A + B + A – B = 60° + 30°
2A = 90°
A = 45°
A + B = 60°
B = 60° – A 
B = 60 – 45°
B = 15°