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

In this problem we need not to take any hard work or solutions if we just use some basic knowledge. We know that cos90=0. We found our answer because 0 multiplied by anything is 0.

Complete step-by-step answer:
Given that
$\cos 10.\cos 20.\cos 30........\cos 900.....\cos 1790$
We have to find the value of this term.
If we observe that the series is $\cos 10.\cos 20.\cos 30\cos 40\cos 50........\cos 900.....\cos 1790$
And the same way there will be a term $\cos 90$.
And we know that $\cos {90^ \circ } = 0$.
Any number multiplied by 0 ,the answer is 0 only.
$\cos 10.\cos 20.\cos 30........\cos 900.....\cos 1790 = 0$
So the correct answer is option B.

Note: Sometimes the problem looks very long and lengthy but it is very easy to solve the one like above. But we may think of applying the formulas or ant identity. But observe that it is a product of such n terms that can be a possibly tricky answer. So observe before we start solving!