First slide

Trigonometric Identities

Question

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

Easy

A

3
B

1
C

2
D

0

Solution

$\log_{3} \tan 1^{\circ} \tan 2^{\circ} \dots \tan 44^{\circ} \tan 45^{\circ} \cot 44^{\circ} \dots \cot 1^{\circ} = \log_{3} 1 = 0$
$1^{\circ} = \log_{3} 1 = 0$

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