If 3tanθ = 2√3sin, 0° < θ < 90°, then the value of cose c^22 + ^22 ^2 + ^2 is:

Answer: Option C

$$\begin{array}{rl}& 3\tan \theta =2\sqrt{3}\sin \theta \\ & \cos \theta =\frac{\sqrt{3}}{2}=\frac{B}{H}\\ & P=\sqrt{3^2+2^2}=\sqrt{13}\\ & \cos \theta =\cos 30^{\circ }\\ & \theta =30^{\circ }\\ & \Rightarrow \frac{\text{cose}{\text{c}}^{2}2\theta +{\cot }^{2}2\theta }{{\sin }^2\theta +{\tan }^{2}2\theta }\\ & =\frac{\text{cose}{\text{c}}^2{60}^{\circ }+{\cot }^2{60}^{\circ }}{{\sin }^2{30}^{\circ }+{\tan }^2{60}^{\circ }}\\ & =\frac{\frac{4}{3}+\frac{1}{3}}{\frac{1}{4}+3}\\ & =\frac{\frac{5}{3}}{\frac{13}{4}}\\ & =\frac{20}{39}\end{array}$$