Question

The value of $\sin {10}^o\sin {30}^o\sin {50}^o\sin {70}^o$ is:

• A. $\frac{1}{36}$
• B. $\frac{1}{32}$
• C. $\frac{1}{18}$
• D. $\frac{1}{16}$

Answer 1

The correct option is D $\frac{1}{16}$

As we know that

$\sin A\sin ({60}^{\circ }-A)\sin ({60}^{\circ }+A)=\frac{1}{4}\sin 3A$

Put $A={10}^{\circ }$

So $\sin {10}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }=\frac{1}{4}\sin {30}^{\circ }=\frac{1}{8}$

So $\sin {10}^{\circ }\sin {30}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }=\sin {30}^{\circ }\left(\sin {10}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }\right)=\frac{1}{2}\times \frac{1}{8}=\frac{1}{16}$