$tan 5 tan 25 tan 30 tan 65 tan 85$ is equal to

3

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\sqrt 3

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1

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\frac{1}{\sqrt 3}

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Solution

The correct option is D $\frac{1}{\sqrt 3}$
Correct option : D. We know that, $tan θ cot θ = 1$ , $tan θ = cot (90 - θ)$ and $cot θ = tan (90 - θ)$ $\begin{matrix} ∴ tan 5 tan 85 tan 25 tan 65 tan 30 & = tan 5 cot (90 - 85) tan 25 cot (90 - 65) tan 30 = tan 5 cot 5 tan 25 cot 25 tan 30 = 1 \cdot 1 \cdot \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} \end{matrix}$

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