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

1.	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» \(\sqrt3(\frac{1}{tanx}+tanx)\) = 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

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»

\(\sqrt3(\frac{1}{tanx}+tanx)\) = 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