Solve limit (as x approaches 0) of 1

I am trying to lớn solve this equation , but i get different answers from the book. Can someone help me please?How to solve


My answers is : $x=45^circ+90^circ k$, $x=pmfrac12 +360^circ k$

Book"s answer: $pm60^circ+360^circ k$ , $45^circ+90^circ k$



Notice, $$cos x-cos 2x+cos 3x=0$$ $$(cos x+cos 3x)-cos 2x=0$$$$2cosleft(fracx+3x2 ight)cosleft(fracx-3x2 ight)-cos 2x=0$$

$$2cos 2xcos x-cos 2x=0$$$$cos 2x(2cos x-1)=0 $$Now, solving for $x$ as follows $$cos 2x=0implies 2x=(2k+1)fracpi2$$$$x=(2k+1)fracpi4$$$$ colorredx=90^circ k+45^circ$$or $$2cos x-1=0$$$$ cos x=frac12=cos fracpi3$$$$x=2kpipmfracpi3$$$$colorredx=360^circ kpm 60^circ$$Where, $colorbluek$ is any integer


First we need to simplify $cos(x)-cos(2x)+cos(3x)=0$.

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Split lớn two equations:

$2cos(x)-1=0$ or $2cos^2(x)-1=0$

And it"s easy lớn solve:

$x=fracpi3+2pi C_1$ ;

$x=frac5 pi 3+2pi C_2$ ;

$x=fracpi4+2 pi C_3$ ;

$x=frac7pi4+2 pi C_4$.

$C_1,C_2,C_3,C_4 in ccevents.vnbbZ $



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