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Question

Let A and B (where A>B), be acute angles. If sin(A+B)=1213 and cos(AB)=35, then the value(s) of sin(2A) is/are
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A
5665
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B
1665
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C
5665
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D
1665
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Solution

The correct option is B 1665
sin(A+B)=1213
So, A+B lies in first or second quadrant,
cos(A+B)=±513
cos(AB)=35
A,B are acute angles and A>BAB lies in the first quadrant,
sin(AB)=45
Now,
sin(2A)=sin(A+B+AB)=sin(A+B)cos(AB)+cos(A+B)sin(AB)=1213×35±513×45=3665+2065 or 36652065=5665 or 1665

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