The value of 10^30^50^70^ is:

Question

The value of $\sin10^\circ\sin30^\circ\sin50^\circ\sin70^\circ$ is:

Accepted Answer

Using $\sin(60^\circ+A)\sin(60^\circ-A)\sin A = \dfrac14\sin3A$ with $A=10^\circ$:

$$\sin10^\circ\sin50^\circ\sin70^\circ = \frac14\sin30^\circ = \frac18$$

$$\sin10^\circ\sin30^\circ\sin50^\circ\sin70^\circ = \frac18\times\frac12 = \frac1{16}$$

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