Ask Me Help Desk - Prove: csc theta - cot theta = sin theta/1+cos theta

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Prove: csc theta - cot theta = sin theta/1+cos theta

I'm trying to prove that csc theta minus cot theta equals sin theta/1+cos theta, but I get 1-cos theta/sin theta. Where am I going wrong?

I do not know where you're going wrong. You have not shown what you tried.

$csc(x)-cot(x)$

$=\frac{1}{sin(x)}-\frac{cos(x)}{sin(x)}$

$=\frac{sin(x)-sin(x)cos(x)}{sin^{2}(x)}$

$=\frac{sin(x)(1-cos(x))}{sin^{2}(x)}$

$=\frac{1-cos(x)}{sin(x)}$

Now, multiply top and bottom by
1+cos(x) and you should see it fall into place.

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