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


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Question Number 35877 by 0123456789 last updated on 25/May/18

$If \cos A = \frac{3}{4}, then 32 \sin (\frac{A}{2}) \sin (\frac{5 A}{2}) =$
	Answered by tanmay.chaudhury50@gmail.com last updated on 25/May/18
	$32sin((A/2))sin(((5A)/2)) =16×(cos2A−cos3A) =16×{(2cos^2 A−1)−(4cos^3 A−3cosA)} =16×{(((18)/(16))−1)−(4×((27)/(64))−(9/4))} =16×{((1/8))−(((27)/(16))−(9/4))} =16×{(1/8)−(((27−36)/(16)))} =16×{((2+9)/(16))} =11$
	$32 s i n (\frac{A}{2}) s i n (\frac{5 A}{2})$ $= 16 \times (c o s 2 A - c o s 3 A)$ $= 16 \times {(2 {c o s}^{2} A - 1) - (4 {c o s}^{3} A - 3 c o s A)}$ $= 16 \times {(\frac{18}{16} - 1) - (4 \times \frac{27}{64} - \frac{9}{4})}$ $= 16 \times {(\frac{1}{8}) - (\frac{27}{16} - \frac{9}{4})}$ $= 16 \times {\frac{1}{8} - (\frac{27 - 36}{16})}$ $= 16 \times {\frac{2 + 9}{16}}$ $= 11$
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