F asked in Science & MathematicsMathematics · 6 months ago

# Find all solutions to the given equation in the interval [0,2π). Give the exact solution, including "pi" for π. 4cotx+4sqrt(3)=0?

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• 6 months ago

4cot(x)+4sqr(3)=0, 0=<x<2pi

=>

tan(x)=-1/sqr(3)

=>

x=5pi/6, or x=11pi/6

• 6 months ago

4cotx + 4√3 = 0

so, cotx = -√3

i.e. tanx = -1/√3....negative means Q2

Then, x = -π/6 + nπ...for n = 0, 1, 2,...

or, x = (π/6)(6n - 1)

Hence, for n = 0 and 1 we have:

x = -π/6, 5π/6 and 11π/6

so, x = 5π/6 and 11π/6 are solutions for [0, 2π)

:)>

• Vaman
Lv 7
6 months ago

4cotx+4sqrt(3)=0,  cot x +sqrt 3=0, cot x +2 sqrt 3/2=0

cot x + 2 sin 60=0, 1/2 cos x/ sin x +sin 60=0

cos 60 sin x + sin 60 cos x=0

sin(x+60)=0= sin pi. pi= x+60, x= 180-60=120. This is the answer.

• 6 months ago

Given --

4 cot x + 4 √3  =  0

Divide both the sides by 4 ---

=>  cot x + √3  =  0

=> cot x  =  -  √3

=> tan x  =  - ( 1/√3 )

tan has negative values in 2nd and 4th Quadrants.

=>  x  =  (5/6) pi  and (11/6) pi  ................ Answer