How to solve the equation `sqrt(3)sin x-cosx=0` ?

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`sqrt(3)sinx-cosx=0`

`sqrt(3)/2 sinx-(1/2)cosx=0`

`sin(pi/3) sinx-cos(pi/3)cosx=0`

`cos(x+pi/3)=cos(2n pi+pi/2)`

`x+pi/3=2n pi+pi/2`

`x=2n pi+(pi/2-pi/3)`

`x=2n pi+pi/6`

Ans.

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`sqrt(3)*sinx - cosx = 0`

`or, (sqrt(3)/2)*sinx - (1/2)*cosx = 0`

`or, cos(30)*sinx - sin(30)*cosx = 0`

`or, sin(x-30) = 0`

`or, sin(x-30) = sin(n*pi)`

`or, ` `or, x-30 = n*pi`

`or, x = n*pi + 30`

`or, x = n*pi + pi/6`

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