If $$\sqrt{3}$$ tanA = 3 sinA, find the value of $$(2\sqrt{3} \cosec A×\tan A)$$​​

Correct option is A

Given: ​

$$\sqrt{3}$$​ tanA = 3sinA 

To find: $$(2\sqrt{3} \cosec A×\tan A)$$ 

Solution: ​

​$$\sqrt3\tan A = 3 \sin A \\ \ \\ \sin A = \frac{\sqrt3 \tan A}{3} \\ \ \\ \implies \cosec A = \frac{3}{\sqrt3 \tan A}$$ 

Now, putting this into the expression;

​$$2\sqrt{3} \cosec A×\tan A \\ \ \\ = 2\sqrt{3}\times \frac3{\sqrt3\tan A}×\tan A \\ \ \\ = 6$$​​