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Question
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
Options
- \[\frac{1}{\sqrt{2}}\]
0
1
-1
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Solution
\[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\]
\[ = \cos1^\circ \cos2^\circ \cos3^\circ . . . \cos90^\circ . . . \cos179^\circ\]
\[ = 0 \left( \cos90^\circ = 0 \right)\]
Hence, the correct answer is option 0.
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