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I've been trying to solve this for 1hour, but I can't do it. I don't know if I'm missing something or it just doesn't open to me...

Simplify the following expression:

$$\frac{\sin^2 x - \cos^2 x}{ \sin x - \cos x}$$

Help will be appreciated.

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Factor the numerator ($a^2-b^2=(a+b)(a-b)$). – David Mitra Jan 17 '12 at 22:51
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Thank You, now it seems so obvious. I don't know what I was thinking. – JanL Jan 17 '12 at 23:01
Your welcome; glad to help. – David Mitra Jan 17 '12 at 23:07

2 Answers

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It's $\sin(x)+\cos(x)$. Follow Mitra's hint!

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up vote 2 down vote

It might further be simplified to $\sqrt{2}\sin(x + \pi/4)$.

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