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The value of $\tan 5^{\circ} \tan 10^{\circ} \tan 15^{\circ} \dots \tan 85^{\circ}$ is

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0

Not defined

1

- 1

answer is C.

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Detailed Solution

Given expression is

\tan 5^{\circ} \tan 10^{\circ} \tan 15^{\circ} \dots \tan 85^{\circ}

.
We know,

tanx = \cot (90^{\circ} - x)

and

tanx . cotx = 1

.
We get,

\tan 5 . \tan 10 . \tan 15 \dots \tan 80 . \tan 85

= \tan 5 . \tan 10 . \tan 15 \dots \tan 45 . \cot \cot (90 - 35) \dots \cot \cot (90 - 10) \cot (90 - 5)

After rearranging terms,

= \tan 5 . \cot 5 . \tan 10 . \cot 10 . . . \tan 45 = 1

.
Hence, the correct option is (3).

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