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.