Which is the answer for this trigonometric ecuation: cosx+cos2x=0?

Question

is try to get which angles are according to that ecuation in while 0_

Answer 1

Look at the various values of cosx when x = pi/2, pi, etc. (recall that pi/2 = 90 degrees).

From looking at these values in my book, I see two values for x that will satisfy this equation: x=pi/3, and x=pi

cos pi/3 = 1/2
cos 2pi/3 = -1/2

cos pi = -1
cos 2pi = 1

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Answer 2

Since cos2x=cos^2(x)-sin^2(x)=2cos^2(x)-1,
cos(x)+cos2x=0 is the same as
cos(x)+2cos^2(x)-1=0
let p=cosx
this transforms the above to equation to p+2p^2-1=0
This factors as (2p-1)(p+1)=0
Therefore, p=.5 or p=-1
Therefore, cos(x)=.5 or cos(x)=-1
The first case occurs in your stated domain when x=60 or 300 degrees; the second case happens when x=180 degrees.

Answer 3

Let's see;
cosx+cos2x=0 or cosx+(cos^2-sin^2)=0
cos^2x+cosx-(1-cos^2x)=0
2cos2x+cosx-1=0
(2cos^x-1)(cosx+1)+0
x=arcos45 ; x=arc180

cos'x=1/2 (acceptable), cos''x=-1(imp)

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Answer 4

you might want to use cos2x equation from the book
and then try to solve it