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I'm trying to solve this problem but I can't figure how. Can you help me?

$A=\frac{\sin \alpha+\cos(3\pi/2-\alpha)+\tan(5\pi+\alpha)}{\csc(2\pi-\alpha)+\sin(5\pi/2+\alpha)}$

If $\tan \alpha=-2/3$ and $\alpha \in$ IV quadrant, calculate the value of the expression.

Thanks.

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    Can somebody help?2012-03-26

1 Answers 1

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You can find $\cos(\alpha)$ from the identity $\sec^2(\alpha) = \tan^2(\alpha) + 1$ and the fact that $\alpha$ is in QIV. Then find the sine. After that use angle sum/difference formulas to simplify terms that involve a trig function of a sum or difference. For example, $\cos(3\pi/2 - \alpha) = \cos(3\pi/2)\cos(\alpha) + \sin(3\pi/2)\sin(\alpha) = -\sin(\alpha)$. It's a bit messy but I don't see an easier solution to the problem.