Solve the equation $cos2x-cosx=0$ ?

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Answer 1 · 2017-04-04T12:51:53

$x=(2n+1)pi$ or $x=2npi+-(2pi)/3$ , where $n$ is an integer

Using identity $cos2x=2cos^2x-1$ , $cos2x-cosx=0$ can be written as

$2cos^2x-cosx-1=0$ and hence using quadratic formula

$cosx=(-(-1)+-sqrt((-1)^2-4xx2xx(-1)))/(2xx2)$

$=(1+-sqrt9)/4$

$=(1+-3)/4$

$=1$ or $-1/2$

If $cosx=1$ , $x=(2n+1)pi$ , where $n$ is an integer

and if $cosx=-1/2$ , $x=2npi+-(2pi)/3$ , where $n$ is an integer

Solve the equation cos2x-cosx=0cos2x-cosx=0?