Question

If 2 sin (A + B) = `sqrt3` and cos (A − B) = 1, then find the measures of angles A and B. 0 ≤ A, B, (A + B) ≤ 90°.

Answer 1

2 sin (A + B) = `sqrt3`

⇒ sin (A + B) = `sqrt3/2`

⇒ sin (A + B) + sin 60

A + B = 60         ...(i)

cos (A − B) = 1

cos (A  B) = cos 0

A − B = 0        ...(ii)

Adding (i) and (ii) 

2A = 60

A = 30°

From (i)

30 + B = 60

B = 30°

∠A = 30°, ∠B = 30°