How Can You Further Simplify 2cos2x - 2cosx in Trigonometry?

[kavipach]

Homework Statement

2cos2x-2cosx...how do you simplify this further?

Homework Equations

The Attempt at a Solution

2(cos2x-cosx)..but i have to find 0=2cos2x-2cosx so this doesn't really help me.

 

[Office_Shredder]

You're trying to find when 2cos(2x)-2cos(x)=0? Start by what you did... you want to find x such that cos(2x)=cos(x). Hint: cosine is periodic

 

[kavipach]

would it be pi/2 and 3pi/2?

 

[queenofbabes]

nope...maybe try drawing cos(2x) and cos(x)?

 

[zcd]

$$\cos(2x)=2\cos^{2}(x)-1$$, so $$2\cos(2x)-2\cos(x)=2\cos^{2}(x)-1\cos(x)-1=0$$. Factoring yields $$(2\cos(x)+1)(\cos(x)-1)=0$$