Monday, 18 March 2013

trigonometry - Solving $cos(x/2) = sin x$



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.



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



Thanks!


Answer



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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