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If cosA=3/4, then 32 sin, A/2 sin, (5A)/...

If `cosA=3/4, then 32 sin, A/2 sin, (5A)/2=` (A) `sqrt(11)` (B) `-sqrt(11) (C) 11 (D) -11

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Verified by Experts

The correct Answer is:
11
`32sin((A)/(2))sin((5A)/(2))`
`=16(cos((A)/(2)-(5A)/(2))-cos((A)/(2)+(5A)/(2)))`
`=16(cos 2A-cos3A)`
`=16(cos 2A-cos3A)`
`=16(2cos^(2)A-1-4cos^(3)A+3cosA)`
Now, putting the value of `cosA=3//4`, we get
`32sin((A)/(2))sin((5A)/(2))=11`.
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