If 3 cotA = 2, then find the value of $$\sqrt{\frac{3(\cosec^2 A - 1)}{(\sec^2 A - 1)}}.$$​

Correct option is C

Given: ​

3cotA = 2 

To find; $$\sqrt{\frac{3(\cosec^2 A - 1)}{(\sec^2 A - 1)}}$$ 

Solution: ​

​$$\cot A = \frac{3\rightarrow base}{2\rightarrow perpendicular}$$ 

Then ,  

Hypotenuse = $$\sqrt{(3)^2 +(2)^2} = \sqrt{13}$$​​

Now using in expression;

​$$\sqrt{\frac{3(\cosec^2 A - 1)}{(\sec^2 A - 1)}} \\ \ \\ = \sqrt{\frac{3(({\frac{\sqrt{13}}{3})}^2 - 1)}{({\frac{\sqrt{13}}{2}}^2) - 1}} \\ \ \\ = \sqrt{ \frac{3(\frac{4}{9})}{\frac{9}{4}}} \\ \ \\ =\sqrt{\frac{12}{9}\times \frac{4}{9}} \\ \ \\ = \frac{4\sqrt3}{9}$$​​