Question

Find the value of $\sin 2^{\circ }\sin 4^{\circ }\sin 6^{\circ }........\sin {180}^{\circ }$ .

Answer 1

Hint: Angles of $\sin$ are written in multiplication and we know that $\sin {180}^{\circ }=0$
We need to find the value of $\sin 2^{\circ }\sin 4^{\circ }\sin 6^{\circ }........\sin {180}^{\circ }$ . Observe that all these angles of $\sin$ are written in multiplication and we know that $\sin {180}^{\circ }=0$ . When 0 is multiplied by anything, the result is 0 only. So, the value of given expression will be 0.
Note: We should remember some basic trigonometric ratios.