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If sin(A - B) = 1 2 and cos(A + B) = 1 2 , find A and B. - Mathematics

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Question

If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.

Sum
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Solution

sin(A - B) = `(1)/(2)`

⇒ sin(A - B) = sin30°
⇒ A - B = 30° ......(i)
cos(A + B) = `(1)/(2)`
⇒ cos(A + B) = cos60°
⇒ A + B = 60° ........(ii)
Adding (i) and (ii)
A - B + A + B = 30° + 60°
⇒ 2A = 90°
⇒ A = 45°
Substituting value of A in (i)
A - B = 30°
45° - B = 30°
B = 15°
Therefore,
A = 45° and B = 15°.

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Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.1

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Frank Mathematics [English] Class 9 ICSE
Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.1 | Q 25
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