How do you find all values of x in the interval [0, 2pi] in the equation $cos(2x)+cos(x)=2$ ?

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Answer 1 · 2016-04-18T21:49:18

$S=2pin$

Use the Property: $cos2A=2cos^2A-1$

$2cos^2x-1+cosx=2$

$2cos^2x+cosx-3=0$

$(2cosx+3)(cosx-1)=0$

$cosx=-3/2 or cosx=1$

$x=cos^-1(-3/2) or x=cos^-1 1$

$x=$ undefined, $x=2pin$

$S=2pin$

How do you find all values of x in the interval [0, 2pi] in the equation cos(2x)+cos(x)=2cos(2x)+cos(x)=2?