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What is the root x in equation square root 3 cos x - sin x = 0?

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yapayapa | Honors

Posted July 20, 2013 at 1:40 PM via web

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What is the root x in equation square root 3 cos x - sin x = 0?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 20, 2013 at 1:51 PM (Answer #1)

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Supposing that you need to solve for x the equation `sqrt3*cos x - sin x = 0` , it is indicated to divide the equation both sides by `cos x` or by `sin x` .

Selecting the option to divide the equation by `cos x` yields:

`sqrt 3 - sin x/cos x = 0`

Using the trigonometric identity `sin x/cos x = tan x` yields:

`sqrt 3 - tan x = 0 => tan x = sqrt 3`

`x = tan^(-1)sqrt 3 + n*pi`

`x = pi/3 + n*pi`

Hence, evaluating the general solution to the given equation, yields `x = pi/3 + n*pi` .

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