How to solve Cos(3x)-Cos(2x)+Cos(x)=0 ?

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Answer 1 · 2018-07-06T01:17:49

$cos (3 x) - cos (2 x) + cos (x) = 0$ $Cos(3x)-Cos(2x)+Cos(x)=0$

$\Rightarrow cos (3 x) + cos (x) - cos (2 x) = 0$ $=>Cos(3x)+Cos(x)-Cos(2x)=0$

$\Rightarrow 2 cos (2 x) cos (x) - cos (2 x) = 0$ $=>2Cos(2x)Cos(x)-Cos(2x)=0$

$\Rightarrow cos (2 x) (2 cos (x) - 1) = 0$ $=>Cos(2x)(2Cos(x)-1)=0$

When
$cos 2 x = 0$ $cos2x=0$

$=>2x=(2n+1)pi/2" where " ninZZ$

$=>x=(2n+1)pi/4" where " ninZZ$

When

$(2Cos(x)-1)=0$

$cos(x)=1/2=cos(pi/3)$

$=>x=2kpipmpi/3"where "k in ZZ$