If tan θ = 3 and θ lies in third quadrant,

C. – 3/√10

Explanation:

According to the question,

Given that, tan θ = 3 and θ lies in third quadrant

⇒ cot θ = 1/3

We know that,

Cosec2θ = 1+cot2θ

$=1+\left(\frac{1}{3}\right)^{2}=1+\frac{1}{9}=\frac{10}{9}$

$\Rightarrow \sin ^{2} \theta=\frac{9}{10}$

$\Rightarrow \sin \theta=\pm \frac{3}{\sqrt{10}}$

$\Rightarrow \sin \theta=-\frac{3}{\sqrt{10}}$, since $\theta$ lies in third quadrant.

Thus, option (C) – 3/√10 is the correct answer.