If tanθ + cotθ = 2, then the value if tan¹⁰⁰θ + cot¹⁰⁰θ is?

A. 2

B. 0

C. 1

D. $$\sqrt 3 $$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{tan}}\theta + {\text{cot}}\theta = 2 \cr & {\text{Put }}\theta = {45^ \circ } \cr & 1 + 1 = 2\left( {{\text{matched}}} \right) \cr & {\text{So, }}\theta = {45^ \circ } \cr & \Rightarrow {\text{ta}}{{\text{n}}^{100}}{45^ \circ } + {\text{co}}{{\text{t}}^{100}}{45^ \circ } \cr & \Rightarrow {1^{100}} + {1^{100}} \cr & \Rightarrow 2 \cr} $$