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Can anyone give me just a hint as to how to go about solving this? Yes it is for homework, but I don't want an answer, just a bit of guidance. I'm thinking the half angle formula for the first bit, but it doesn't seem to look right.

$$\cos(x/2)-\sin(x) = 0$$


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up vote 5 down vote accepted

Let $y=\frac{x}{2}$, so that your equation is $$\cos(y)=\sin(2y).$$ Do you know any formulas that you can use here?

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Thanks! That was just what I needed to get the brain started :) – Josh Jul 19 '11 at 0:32
No problem, glad I could help :) – Zev Chonoles Jul 19 '11 at 0:33

You could also try rewriting $\sin x$ as $$\sin x =2\sin \frac{x}{2}\cos\frac{x}{2}.$$

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