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

If `sin (A - B) = 1/2 and cos (A + B) = 1/2` where A > B > 0 and A + B is an acute angle, then the value B is

A

`pi/6`

B

`pi/12`

C

`pi/4`

D

`pi/2`

Text Solution

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The correct Answer is:
To solve the problem, we start with the given equations: 1. \( \sin(A - B) = \frac{1}{2} \) 2. \( \cos(A + B) = \frac{1}{2} \) We also know that \( A > B > 0 \) and \( A + B \) is an acute angle. ### Step 1: Solve for \( A + B \) From the second equation, we know that: \[ \cos(A + B) = \frac{1}{2} \] The cosine of an angle is \( \frac{1}{2} \) at \( 60^\circ \) (or \( \frac{\pi}{3} \) radians). Since \( A + B \) is an acute angle, we can conclude: \[ A + B = 60^\circ \]
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