First slide

Trigonometric Identities

Question

The value of $\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \dots \tan 89^{\circ}$ is

Easy

A

1
B

0
C

$\infty$
D

1/2

Solution

We have,
$\begin{array}{l} \tan 89^{\circ} = \tan (90^{\circ} - 1^{\circ}) = \cot 1^{\circ} \\ \tan 88^{\circ} = \tan (90^{\circ} - 2^{\circ}) = \cot 2^{\circ} etc \\ ∴ \tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \dots \tan 88^{\circ} \tan 89^{\circ} \\ = \tan 1^{\circ} \tan 2^{\circ} \dots \tan 45^{\circ} \cot 44^{\circ} \cot 43^{\circ} \dots \cot 2^{\circ} \cot 1^{\circ} \\ = 1 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App