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Question
If 2 cos (A + B) = 2 sin (A - B) = 1;
find the values of A and B.
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Solution
2 cos (A + B) = 1
cos (A + B) = `(1)/(2)`
cos (A+B) = cos 60°
A + B = 60° ........( 1)
2 sin (A – B) = 1
2 sin (A – B) = `(1)/(2)`
A – B = 30° ........(2)
Adding (1) and (2)
A + B + A – B = 60° + 30°
2A = 90°
A = 45°
A + B = 60°
B = 60° – A
B = 60 – 45°
B = 15°
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