Question

If sin(A − B) = `1/2` and cos(A + B) = `1/2`, 0° < A + B < 90° and A > B, then find the values of A and B.

Answer 1

sin(A − B) = `1/2`

sin(A − B) = sin 30° `...[∵ sin 30° = 1/2]`

A − B = 30°   ....(i)

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

cos(A + B) = cos 60° `...[∵ cos 60° = 1/2]`

A + B = 60°   ....(ii)

Adding (i) and (ii), we get,

A − B + A + B = 30 + 60°

2A = 90°

A = `(90°)/2`

A = 45°

Putting the value of A in the equation (i).

A − B = 30°

45° − B = 30°

B = 45° − 30°

B = 15°

Hence, A = 45° and B = 15°.