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Question

Prove that:
$$ \sin\,10^{\circ}\,\sin\,50^{\circ}\,\sin\,60^{\circ}\,\sin\,70^{\circ}  = \dfrac{\sqrt{3}}{16}$$


Solution

We know that 

$$4sin\theta sin(60^0+\theta)sin(60^0-\theta)=sin3\theta$$

So, 

$$sin10^osin70^osin50^osin60^o$$

$$=\dfrac{1}{4}sin(10\times3)^0\times\sin60^o$$

$$=\dfrac{\sqrt{3}}{16}$$

Mathematics

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