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The value of 16 sin 44° sin 108° sin 72° sin36° is equal to

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Solution

We have,
$\begin{array}{l} 16 \sin 144^{\circ} \sin 108^{\circ} \sin 72^{\circ} \sin 36^{\circ} \\ = 16 \sin 36^{\circ} \cos 18^{\circ} \cos 18^{\circ} \sin 36^{\circ} \\ = 16 \cos^{2} 18^{\circ} \sin^{2} 36^{\circ} = 16 {(\sin 36^{\circ} \cos 18^{\circ})}^{2} \\ = 16 {\{\frac{\sqrt{10 - 2 \sqrt{5}}}{4} \times \frac{\sqrt{10 + 2 \sqrt{5}}}{4}\}}^{2} = 5 \end{array}$

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Multiple and sub- multiple Angles

Remember concepts with our Masterclasses.

The value of 16 sin 44° sin 108° sin 72° sin36° is equal to

We have,16sin⁡144∘sin⁡108∘sin⁡72∘sin⁡36∘=16sin⁡36∘cos⁡18∘cos⁡18∘sin⁡36∘=16cos2⁡18∘sin2⁡36∘=16sin⁡36∘cos⁡18∘2=1610−254×10+2542=5

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