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# The value of $\cos 10\cos 20\cos 30...\cos 900...\cos 1790$ is?A.$\dfrac{1}{{\sqrt 2 }}$B.0C.1D.None of these

Last updated date: 13th Jun 2024
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Hint: First, we will rewrite the given values and then use the cosine value $\cos 90 = 0$, in the obtained value. Then we will simplify the obtained value to find the required value.

We are given that $\cos 10\cos 20\cos 30...\cos 900...\cos 1790$.
$\Rightarrow \cos 10\cos 20\cos 30\cos 40\cos 50\cos 60\cos 70\cos 80\cos 90...\cos 900...\cos 1790$
Using the cosine value $\cos 90 = 0$, in the above equation, we get
$\Rightarrow \cos 10\cos 20\cos 30\cos 40\cos 50\cos 60\cos 70\cos 80 \times 0 \times ...\cos 900...\cos 1790$
$\Rightarrow 0$
Thus, the value of $\cos 10\cos 20\cos 30...\cos 900...\cos 1790$ is 0.
Note: The trick part of this question is to rewrite the given value to reach the $\cos 90 = 0$, in the given problem. In solving these types of questions, the key concept is to have a good understanding of the basic trigonometric values and learn how to use the values from trigonometric tables. Students should have a grasp of trigonometric values, for simplifying the given equation. Avoid calculation mistakes.