How do you find the general solutions for $sinx = √(3)*cosx$ ?

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Answer 1 · 2015-08-30T18:21:46

$x= pi/3+kpi; k in ZZ$

If you divide both sides of the equation by $cosx$ , you get

$tan x=sqrt(3)$

Before you do the division you have to exclude zeos of $cosx$ function from the domain of the equation:

$D=RR-{pi/2+k pi, k in ZZ}$ (1)

This equation has solutions in set given by:

$x= pi/3+kpi; k in ZZ$ (2)

, because $tan (pi/3)=sqrt(3)$ and $tan$ function has a period of $pi$

All points described in (2) are in the domain (1) , so finally the answer is:

$x= pi/3+kpi; k in ZZ$

How do you find the general solutions for sinx = √(3)*cosxsinx = √(3)*cosx?