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Find all possible values of \(\cos(\theta)\) if \(\cos(2\theta) = 2\cos(\theta)\)

 Oct 31, 2019
 #1
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cos theta can be 1/2 and 1.

 Oct 31, 2019
 #2
avatar+110189 
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Why is it a 'challange questions'?

 

 

\(\cos(2\theta) = 2\cos(\theta)\\ cos^2\theta-\sin^2\theta = 2\cos(\theta)\\ cos^2\theta-(1-\cos^2\theta) = 2\cos(\theta)\\ 2cos^2\theta-1 = 2\cos\theta\\ 2cos^2\theta-2\cos\theta-1 = 0\\\)

 

Now let x=cos (theta)  and solve for x.

 

etc

 Nov 1, 2019

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