Question

The smallest value of x satisfying the equation √3 (cot x + tan x) = 4 is 

A. \(\frac{2π}3\)

B. \(\frac{π}3\)

C. \(\frac{π}6\)

D. \(\frac{π}{12}\)

Answer 1

\(\sqrt3(\frac{1}{tanx}+tanx)\) = 4

\(\sqrt3(\frac{1+tan^2x}{tanx})\) = 4

√3+√3 tan²x = 4 tan x 

√3 tan²x - 4 tan x+√3 = 0 

Therefore

tan = √3 or tanx = \(\frac{1}{\sqrt3}\)

Therefore x = \(\frac{π}3\) or \(\frac{π}6\)

But here the smallest angle is \(\frac{π}6\)

Option C