The value of tan10°. tan15°. tan75°. tan80° is?

Answer: Option B

$$\begin{array}{rl}& \tan 10^{\circ }.\tan 15^{\circ }.\tan 75^{\circ }.\tan 80^{\circ }\\ & \Rightarrow \left(\tan {10}^{\circ }.\tan {80}^{\circ }\right).\left(\tan {15}^{\circ }.\tan {75}^{\circ }\right)\\ & \Rightarrow 1\times 1\\ & \left[\text{If tan A}\text{.tan B}=\text{1}\text{. then, A}+\text{B}={90}^{\circ }\right]\\ & \Rightarrow 1\end{array}$$