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If `Sin (A – B) = 1/2` and `Cos (A + B) = 1/2`, `0^@` < a + `B <= 980^@`, a > B Find a and B - CBSE Class 10 - Mathematics

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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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Solution If `Sin (A – B) = 1/2` and `Cos (A + B) = 1/2`, `0^@` < a + `B <= 980^@`, a > B Find a and B Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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