Question

If sin (A – B) = `1/2` and cos (A + B) = `1/2, 0^0 ≤ (A + B) ≤ 90^0` and A > B, then find A and B.

Answer 1

Here, sin (A – B) = `1/2`
`⇒ sin (A – B) = 30^0                    [∵ sin 30^0 = 1/2]`
`⇒ (A – B) = 30^0`                            …….(i)
`Also, cos (A + B) = 1/2`
`⇒ cos (A + B) = cos 60^0              [∵ cos 60^0 = 1/2]`
`⇒ A + B = 60^0`                                    ….(ii)
Solving (i) and (ii), we get:
`A = 45^0 and B = 15^0`