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C3 simple trig question

I have to work out for which values of x, 2cos2x - 2sin x is equal to zero.

How do I approach this problem? I know that I need to find some way of either getting rid of the cos or sin, so that I will be able to factorise the expression, but I'm not sure how to do that.

Any suggestions on how to tackle the problem would be great.

Thank you!
cos⁡2x=cos⁡2x−sin⁡2x\cos 2x = \cos^2 x - \sin^2 x

Form a quadratic in sin x.
I'm still not sure how to go about this since that wouldn't eliminate cos, so I would still be unable to solve it. :confused:
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coldfusion
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Silverwing Sketcher
I'm still not sure how to go about this since that wouldn't eliminate cos, so I would still be unable to solve it. :confused:

Try cos⁡2x=1−2sin⁡2x\cos 2x = 1 - 2\sin^2 x
Silverwing Sketcher
I'm still not sure how to go about this since that wouldn't eliminate cos, so I would still be unable to solve it. :confused:


I assumed you already knew from Core 2 that:

cos⁡2x=1−sin⁡2x\cos^2x =1 - \sin^2x

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