If a = sin frac{pi }{{18}}sin frac{{5pi | vedclass

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Question

$a= \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18} $

$=\sin 10^{\circ} \sin 50^{\circ} \sin 70^{\circ} $

$=\frac{1}{2}\left[2 \

Vedclass · Accepted Answer

$\frac{1}{{\left[ x \right]}}$

Vedclass · Answer

$a= \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18} $

$=\sin 10^{\circ} \sin 50^{\circ} \sin 70^{\circ} $

$=\frac{1}{2}\left[2 \sin 70^{\circ} \sin 10^{\circ}ight] \sin 50^{\circ}$

$=\frac{1}{2}\left[\cos 60^{\circ}-\cos 80^{\circ}ight] \sin 50^{\circ}$

$=\frac{1}{4} \sin 50^{\circ}-\frac{1}{4}\left(2 \cos 80^{\circ} \sin 50^{\circ}ight)$

$=\frac{1}{4} \sin 50^{\circ}-\frac{1}{4}\left(\sin 130^{\circ}-\sin 30^{\circ}ight)$

$=\frac{1}{4} \sin 50^{\circ}-\frac{1}{4} \sin 50^{\circ}+\frac{1}{4} \cdot \frac{1}{2}=\frac{1}{8}$

$y=2[x]+2 	ext { and } y=3[x-2]$

$\Rightarrow 2[\mathrm{x}]+2=3[\mathrm{x}-2]$

$=3[\mathrm{x}]+3[-2] $

$=3[\mathrm{x}]-6 $

$\Rightarrow [\mathrm{x}]=8 $

$	herefore  \mathrm{a}=\frac{1}{[\mathrm{x}]}$

If $a = \sin \frac{\pi }{{18}}\sin \frac{{5\pi }}{{18}}\sin \frac{{7\pi }}{{18}}$ and $x$ is the solution of the equatioin $y = 2\left[ x \right] + 2$ and $y = 3\left[ {x - 2} \right] ,$ where $\left[ x \right]$ denotes the integral part of $x,$ then $a$ is equal to :-

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