Answer:
x= 120°
Step-by-step explanation:
cos(2x)-cos(x)=0
[tex]\Rightarrow 2\cos^2x-\cosx-1=[/tex]0 [as [tex]\cos(2x)=2\cos^2x-1[/tex]]
[tex]\Rightarrow 2\cos^2x-2\cosx +\cosx-1=0[/tex]
[tex]\Rightarrow 2\cos x(\cos x-1) +(\cos x-1)=0[/tex]
[tex]\Rightarrow (\cos x-1)(2\cos x +1)=0[/tex]
[tex]\Rightarrow \cos x-1=0 \;or\; 2\cos x +1=0[/tex]
[tex]\Rightarrow \cos x=1 \;or\; \cos x =-1/2[/tex]
[tex]\Rightarrow x=\cos^{-1}1 \;or\; x =\cos(-1/2)[/tex]
For [tex]x=\cos^{-1}1[/tex] and 0° < x <180°
There is no possible value of x.
For [tex]x =\cos(-1/2)[/tex] and 0° < x <180°
The possible value of x is
x= 120°
