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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.
Solution
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`
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