If tan⁡θ = $$\frac{5}{12}$$​, $$0< θ<\frac{π}2$$​, then the value of $$\frac{\cos ⁡θ +5 \cot⁡θ }{\cosec θ-\cos⁡θ }$$​ will be:

Correct option is C

Given:​

tan ⁡θ =$$\frac{5}{12}$$​, $$0< θ<\frac{π}2$$​​,

To find ; value of   $$\frac{\cos ⁡θ +5 \cot⁡θ }{\cosec θ-\cos⁡θ }$$​​

Formula Used: 

​$$\sin \theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}} = \frac{1}{\cosec \theta}\\ \ \\ \cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}= \frac{1}{\sec \theta}\\ \ \\\tan \theta = \frac{\text{Perpendicular}}{\text{Base}} \quad \text{or} \quad \tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{1}{\cot \theta}$$ 

Solution: 

From the Pythagoras theorem;

​$$h^2 =p^2 +b^2 \\ \ \\ = 5^2+12^2 = 169 \\ \ \\ h = 13$$ 

Now, putting the values ;

​$$\frac{\frac{12}{13} +5 \times \frac{12}{5} }{\frac{13}{5}-\frac{12}{13} } \\ \ \\ = \frac{\frac{12 \times 14}{13}}{\frac{109}{65} } \\ \ \\ = \frac{840}{109}$$​​