Question

Find the value of the equation : $\sin {10}^{\circ }\cdot \sin {50}^{\circ }\cdot \sin {60}^{\circ }\cdot \sin {70}^{\circ }$

Answer 1

$\sin {10}^0.\sin {50}^0.\sin {60}^0.\sin {70}^0=?$

We know that

$\sin \theta .\sin (60-\theta )\sin (60+\theta )=\frac{1}{4}\sin 3\theta$

Using this we can rewrite the expression as

$={\sin 10}^0.\sin ({60}^0-{10}^0).\sin ({60}^0+{10}^0).\sin {60}^0$

$=\frac{1}{4}\sin {30}^0.\sin {60}^0$

$=\frac{1}{4}\times \frac{1}{2}\times \frac{\sqrt{3}}{2}$

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