The value of $$sin$$⁡$$12$$∘$$sin$$⁡$$48$$∘$$sin$$⁡$$54$$∘ is equal to

Now,$$sin$$⁡$$12$$∘$$sin$$⁡$$48$$∘$$sin$$⁡$$54$$∘$$=12cos$$⁡$$36$$∘−$$cos$$⁡$$60$$∘$$cos$$⁡$$36$$∘$$=125+14$$−$$125+14=125$$−$$145+14=5$$−$$132=432=18$$

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The value of $\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$ is equal to

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Solution

Now,
$\begin{array}{l} \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ} \\ = \frac{1}{2} (\cos 36^{\circ} - \cos 60^{\circ}) \cos 36^{\circ} \\ = \frac{1}{2} [\frac{\sqrt{5} + 1}{4} - \frac{1}{2}] [\frac{\sqrt{5} + 1}{4}] \\ = \frac{1}{2} [\frac{\sqrt{5} - 1}{4}] [\frac{\sqrt{5} + 1}{4}] \\ = \frac{5 - 1}{32} = \frac{4}{32} = \frac{1}{8} \end{array}$

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Trigonometric transformations

Remember concepts with our Masterclasses.

The value of sin⁡12∘sin⁡48∘sin⁡54∘ is equal to

Now,sin⁡12∘sin⁡48∘sin⁡54∘=12cos⁡36∘−cos⁡60∘cos⁡36∘=125+14−125+14=125−145+14=5−132=432=18

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The value of $\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$ is equal to