Which of the following is the correct value of tan 10°.tan 20°.tan 60°.tan 70°.tan 80°?

Correct option is B

​$$\begin{aligned}&\textbf{Use identity:} \\&\quad \tan(90^\circ - \theta) = \cot \theta \\[10pt]&\text{So:} \\&\quad \bullet \ \tan 80^\circ = \cot 10^\circ \\&\quad \bullet \ \tan 70^\circ = \cot 20^\circ \\[10pt]&\text{Therefore:} \\&\quad \tan 10^\circ \cdot \tan 20^\circ \cdot \tan 60^\circ \cdot \tan 70^\circ \cdot \tan 80^\circ = \tan 10^\circ \cdot \tan 20^\circ \cdot \tan 60^\circ \cdot \cot 20^\circ \cdot \cot 10^\circ \\[10pt]&\text{Now notice:} \\&\quad \tan 10^\circ \cdot \cot 10^\circ = 1, \quad \tan 20^\circ \cdot \cot 20^\circ = 1 \\[10pt]&\text{So the expression becomes:} \\&\quad 1 \cdot 1 \cdot \tan 60^\circ = \tan 60^\circ = \sqrt{3}\end{aligned}$$​​