If $$tan3θ.tan6θ =1$$​, then the value of $$tan30θ$$​ is:

Correct option is B

Given:

​tan3θ . tan6θ = 1

Identity used:

$$tan(A).tan(90^∘ −A)=1$$​​

Solution:

Comparing the identity used with the given equation:

$$6θ=90^∘-3θ$$

$$6θ+3θ=90^∘$$

$$9θ=90^∘$$

$$θ=10^∘$$ 

then, 

$$tan30\times10^∘=-\sqrt{3}$$

Thus, Option B is correct.​