Expert: Jack Cheng - 12/3/2006

Question
how do you simplify sin/cos+cos/sin identity?

Answer
Hi Brandie,

First, it needs to be sin x and cos x (just sin and cos is meaningless). I almost failed a trig test for doing that. I learned it the hard way; I hope you won't.

Well, let's combine the addition:

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sin x   sin x     cos x   cos x    sin^2 x + cos^2x
(----- * -----) + (----- * -----) = ----------------
cos x   sin x     sin x   cos x      cos x sin x

Since sin^2 x + cos^2 x = 1, we have 1/(cos x sin x).

I hope this helps,
Jack

P.S. cos x sin x can be further changed (note that I didn't say simplified) to (1/2)*sin 2x. So you answer could be 2/sin(2x).