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This has been bugging me all day. It seems like a very straight forward question but for whatever reason, I just cannot get my answer in the right format.

The question reads -

The parametric equations of a curve are

x = sin(2A) + 2sin(A)

y = cos(2A) - 2cos(A), where 0 < A < PI

Show that dy/dx = -(sinA) / (1 + cosA)

The differentiation is fine, I can do that without problems and I checked WolframAlpha to make sure I was correct in that but I just cannot simplify the dy/dx to the required format whatever I do. I keep getting very close in the different ways but never exactly what I need. I would be very grateful if someone could help.

Tip: You need to find dx/dA and dy/dA first then invert dx/dA and multiply them together to get to dy/dx

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    You can use the chain rule $dy/dA=(dy/dx)(dx/dA)$ and solve for $dy/dx$.2011-05-20

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Dear Mark, $dy/dx = \frac{dy/dA}{dx/dA} = \frac{2\sin A - 2 \sin 2A}{2\cos A + 2\cos 2A} = \frac{2}{2}\cdot\frac{\sin A (1- 2\cos A)}{(1+\cos A)(-1+2\cos A)} = -\frac{\sin A}{1+\cos A}$ The result may also be written as $-\tan(A/2)$ because $1+\cos A = 2\cos^2 (A/2)$ while $\sin A = 2\cos(A/2)\sin(A/2)$ and $2\cos(A/2)$ cancels. The procedure in the tip (which includes inversion of the function) is totally unnecessary.

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    My guess is that the tip is asking us to take the reciprocal of $dx/dA$, not to invert it as a function :-)2011-09-02