Solving cos(x) = -cos(2x)

[davidp92]

Homework Statement

How do you solve cosx=-cos2x?

The Attempt at a Solution

I've tried graphing it, but just wasn't able to crack the solutions

Thanks for help!

 

[ehild]

What is the relation between two angles a and b if cos(a)=-cos(b)? Look at the unit circle.

Or use the formula cos(2x)=cos^(x)-sin^2(x)

hild

 

[tensorit]

If you merely want the answer (without proof), type "solve cos(x)=-cos(2x) for x" in wolfram alpha. If you want to figure out the proof, look up the trig formula that let's you express cos(2x) in terms of cos(x). With that substitution, you will have transformed your equation into a quadratic equation, with cos(x) as the unknown, the solution of which is cos(x)=-1 (implying x=-pi) or cos(x)=1/2 (implying x=pi/3 or x=-pi/3). Of course, add any integer multiple of 2pi to these answers to characterize the infinite number of solutions.

 

[SammyS]

or use cos(2x) = 2cos²(x) - 1