The value of sin 15° sin 30° sin 75° is:

Correct option is B

Given:

​$$\sin 15^\circ \cdot \sin 30^\circ \cdot \sin 75^\circ$$​​

Formula Used:

​$$\sin 15^\circ = \frac{\sqrt{6} - \sqrt{2}}{4}, \quad \sin 30^\circ = \frac{1}{2}, \quad \sin 75^\circ = \frac{\sqrt{6} + \sqrt{2}}{4}$$​​

Solution:

​$$\sin 15^\circ \cdot \sin 30^\circ \cdot \sin 75^\circ = \left( \frac{\sqrt{6} - \sqrt{2}}{4} \right) \times \left( \frac{1}{2} \right) \times \left( \frac{\sqrt{6} + \sqrt{2}}{4} \right)$$​​

So,

​$$\frac{1}{2} \times \frac{(\sqrt{6} - \sqrt{2})(\sqrt{6} + \sqrt{2}) }{16} = \frac{1}{2} \times \frac{4}{16} = \frac{1}{8}$$​