Question

If sin(A + B) = 1 and sin(A - B) = \(1\over\sqrt2\), find the value of A and B, known A and B ∈ [0, 90°]
1. 90, 0
2. 67.5, 22.5
3. 37.5, 52.5
4. 7.5, 37.5

Answer 1

Correct Answer - Option 2 : 67.5, 22.5

Calculation:

sin(A + B) = 1

sin(A + B) = sin 90°

A + B = 90°     ....(i)

sin(A - B) = \(1\over\sqrt2\)

sin(A - B) = sin 45°

A - B = 45°     ....(ii)

Adding (i) and (ii) we get,

2A = 135°

A = 67.5°

Putting that in equation (i)

67.5 + B = 90°

B = 22.5°