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Question: Find the value of \(\sin {2^ \circ }\sin {4^ \circ }\sin {6^ \circ }........\sin {180^ \circ }\) ....

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

Explanation

Solution

Hint: Angles of sin⁡\sin are written in multiplication and we know that sin⁡180∘=0\sin {180^ \circ } = 0
We need to find the value of sin⁡2∘sin⁡4∘sin⁡6∘........sin⁡180∘\sin {2^ \circ }\sin {4^ \circ }\sin {6^ \circ }........\sin {180^ \circ } . Observe that all these angles of sin⁡\sin are written in multiplication and we know that sin⁡180∘=0\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.