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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

ConceptTrigonometric Ratios of an Acute Angle of a Right-angled Triangle

#### 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^@

Is there an error in this question or solution?

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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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