Question

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

• A. $\frac{1}{8}$
• B. $\frac{1}{16}$
• C. $\frac{\sqrt{3}}{8}$
• D. $\frac{\sqrt{3}}{16}$

Answer 1

Answer: (B)

$\frac{1}{16}$

We, know that

$sinx.sin({60}^o-x).sin({60}^o+x)=\frac{sin3x}{4}$

Here, $x={10}^o$

According to question,

$sin{30}^{o}sin{10}^{o}sin{50}^{o}sin{70}^o$

$⟹\frac{1}{2}.\frac{sin(3\times {10}^o)}{4}$

$⟹\frac{1}{16}$