First slide

Trigonometric Identities

Question

The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \dots \cos 179^{\circ}$ is

Easy

A

$\frac{1}{\sqrt{2}}$
B

0
C

1
D

none of these

Solution

We have,
$\begin{array}{l} \cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \dots \cos 179^{\circ} \\ = \cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \dots \cos 90^{\circ} \dots \cos 179^{\circ} \\ = 0 [∵ \cos 90^{\circ} = 0] \end{array}$

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