If cot 35° = 2-$$\sqrt3$$​ then the value of tan 35° cot 55° + tan 55° cot 35° is:

Correct option is A

Given:
cot 35° = 2-√3
Formula Used:
cot(90-θ)= tan θ
tan (90-θ)= cot θ
tanθ= $$\frac1{cot θ}$$

​​Solution:​
cot 35°= 2-$$\sqrt 3$$​​
tan 35°= $$\frac1{cot 35 \degree}$$= $$\frac{1}{2 - \sqrt{3}} \cdot \frac{2 + \sqrt{3}}{2 + \sqrt{3}}= {\frac{2 + \sqrt{3}}{4 - 3}}$$​
tan 35°=$$2 + \sqrt{3}$$​
= tan 35° cot 55° + tan 55° cot 35°
= tan35° .cot (90-35)° +tan (90-35)° cot 35°
= tan35° .tan 35° + cot 35° . cot 35°
​$$= (\tan 35)^{2} + (\cot 35)^{2} \\= (2+\sqrt{3})^{2} + (2-\sqrt{3})^{2} \\= (4 + 4\sqrt{3} + 3) + (4 - 4\sqrt{3} + 3) \\= 4 + 3 + 4 + 3 = 14$$​​