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I am trying to solve an orbital problem concerned with analytically calculating the solstice points of an orbit. I have managed to reach a point in the problem where I need to simplify the trigonometric expression $$\frac{e \sin^2\theta + \cos\theta}{\sin\theta - e \sin\theta \cos\theta}$$

If someone could give me some tips, that would be great.

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    The only simplification I can see is dividing through the numerator and denominator by $\sin \theta$, which is fairly minor. I'm almost sure that without specifying a particular value of $e$ you will not be able to get anything more simple than that. Is there a specific form of expression you want to get?2012-09-13

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