Find the value of $$\frac{(3 + 3\tan^2 A)\cot A}{(1 + \cot^2 A)\sec A}$$.​

Correct option is C

Given: ​

​$$\frac{(3 + 3\tan^2 A)\cot A}{(1 + \cot^2 A)\sec A}$$ 

Formula Used: ​

​$$1+\tan^2A = \sec^2 A \\ \ \\ 1 +\cot^2A = \cosec^2A$$ 

Solution: ​

​$$\frac{(3 + 3\tan^2 A)\cot A}{(1 + \cot^2 A)\sec A} \\ \ \\ = \frac{3(1 + \tan^2 A)\cot A}{\cosec^2A \times\sec A} \\ \ \\ = \frac{3(\sec^2 A)\cot A}{\cosec^2A \times\sec A}\\ \ \\ = \frac{3(\sec A)\times\frac{\cosec A}{\sec A}}{\cosec^2A }\\ \ \\ = \frac{3\cosec A}{\cosec^2A } = 3\sin A$$​​