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Question
If `sin (A – B) = 1/2` and `cos (A + B) = 1/2`, `0^@` < A + `B <= 90^@`, A > B Find A and B.
Solution
`sin (A – B) = 1/2` and `cos (A + B) = 1/2`
Now `sin (A - B) = 1/2`
`=> sin (A- B) = sin 30^@`
`=> A - B( = 30^@` ....(1)
And `cos (A + B) = 1/2`
`=> cos (A + B) = cos 60^@`
`=> A + B = 60^@` ...(2)
Adding (1) and (2) we get
`2A = 90^@`
`=> A = 90^@/2 = 45^@`
Put `A = 45^@` in (2 ) we get
`=> 45^@ + B = 60^@`
`=> B = 60^@ - 45^@``
`=>B = 15^@`
Thus `A = 45^@ and B = 15^@`
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