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question mark

The minimum value of (tan(x+ π/6))/tanx is:
  1. 0
  2. ½
  3. 1
  4. 3

Aditya Kartikeya , 10 Years ago
Grade 10
anser 1 Answers
Y RAJYALAKSHMI

Last Activity: 10 Years ago

f(x) = tan(x+ π/6)/tanx = (tanx + 1/sqrt(3)/(1 – tanx/sqrt(3)) * 1/tanx
= [sqrt(3) * tanx + 1 ]/[(sqrt(3) – 1) * tanx]
The extreme points of f(x) are for f ’ (x) = 0
By differenetiationg w.r.t x and equating to 0 , we have 
(sqrt(3) – 1)tanx * sqrt(3) * sec2x – (sqrt(3)* tanx + 1) * (sqrt(3) – 1) * sec2x = 0 
On simplication we get,
sec2x = 0 
=> x = π/2
The value of f(x) at x = π/2 = tan(π/2+ π/6)/tanπ/2 = 0
Ans: 0 
 
 
 

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