$\log \tan 1^{\circ}+\log \tan 2^{\circ}+\ldots . .+\log \tan 89^{\circ}$ is

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

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Application +4 | -1

\log \tan 1^{\circ}+\log \tan 2^{\circ}+\ldots . .+\log \tan 89^{\circ}

View answer and explanation

Correct option: B

Option B (0) is correct because

\log \tan 1^{\circ} + \log \tan 2^{\circ} + \dots + \log \tan 89^{\circ} = \log (\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \dots \cdot \tan 89^{\circ})

. Since

\tan \theta \cdot \tan (90^{\circ} - \theta) = 1

, the product inside the logarithm is 1, and

\log 1 = 0