Question

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

Answer 1

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.

Complete step-by-step answer:
We are given that \[\cos 10\cos 20\cos 30...\cos 900...\cos 1790\].
Rewriting this above equation, we get
\[ \Rightarrow \cos 10\cos 20\cos 30\cos 40\cos 50\cos 60\cos 70\cos 80\cos 90...\cos 900...\cos 1790\]
Using the cosine value \[\cos 90 = 0\], in the above equation, we get
\[ \Rightarrow \cos 10\cos 20\cos 30\cos 40\cos 50\cos 60\cos 70\cos 80 \times 0 \times ...\cos 900...\cos 1790\]
Multiplying the above values, we get
\[ \Rightarrow 0\]
Thus, the value of \[\cos 10\cos 20\cos 30...\cos 900...\cos 1790\] is 0.
Hence, option B is correct.

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.