How do you solve the following equation $cos(x+pi/3)+cosx=0$ in the interval [0, 2pi]?

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Answer 1 · 2016-06-29T07:03:14

$x=npi+pi/3$

$cos(x+pi/3)+cosx=0$ can be expanded to

$cosxcos(pi/3)-sinxsin(pi/3)+cosx=0$

or $cosx/2-sqrt3/2sinx+cosx=0$ or

$3/2cosx=sqrt3/2sinx$

$tanx=(3/2)/(sqrt3/2)=3/2xx2/sqrt3=sqrt3=tan(pi/3)$

Hence $x=npi+pi/3$

How do you solve the following equation cos(x+pi/3)+cosx=0 cos(x+pi/3)+cosx=0 in the interval [0, 2pi]?