Evaluate: 96 root 3 sin pi/48.cos pi/48.cos pi/24.cos pi/ 12.cos pi /6

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Solution

Dear student

$96 \sqrt{3} \sin (\frac{π}{48}) \cos (\frac{π}{48}) \cos (\frac{π}{24}) \cos (\frac{π}{12}) \cos (\frac{π}{6}) = 48 \sqrt{3} \times 2 \sin (\frac{π}{48}) \cos (\frac{π}{48}) \cos (\frac{π}{24}) \cos (\frac{π}{12}) \cos (\frac{π}{6}) = 48 \sqrt{3} \times \sin (\frac{π}{24}) \cos (\frac{π}{24}) \cos (\frac{π}{12}) \cos (\frac{π}{6}) = 24 \sqrt{3} \sin (\frac{π}{12}) \cos (\frac{π}{12}) \cos (\frac{π}{6}) = 12 \sqrt{3} \sin (\frac{π}{6}) \cos (\frac{π}{6}) = 6 \sqrt{3} \sin (\frac{π}{3}) = 6 \sqrt{3} \times \frac{\sqrt{3}}{2} = 9 Identity used : \sin 2 x = 2 sinxcosx$
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