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