Question

simplify (sinx)/(1+cosx)-(1+cosx)/(sinx)

Answer 1

\[\frac{ \sin(x) }{ 1+\cos(x) } - \frac{ 1 + \cos(x) }{ \sin(x) }\]
So, let's add the terms together. To do this, we need to make them have the same denominator.
\[\frac{ \sin(x)\sin(x) }{ (1+\cos(x))(\sin(x)) }-\frac{ (1+\cos(x))(1+\cos(x)) }{ \sin(x)(1+\cos(x)) }\]
Adding them together we get.
\[\frac{ \sin(x)\sin(x)-(1+\cos(x))(1+\cos(x)) }{ (1+\cos(x))\sin(x) }\]
Now, there are some simplifications we can do.
\[\frac{ \sin(x)\sin(x)-1-2\cos(x)+\cos(x)\cos(x) } { (1+\cos(x))\sin(x) }\]

From the unit circle, we also know that sin(x) * sin(x) + cos(x) * cos(x) = 1.

So, what's next?

Answer 2

Ty.

Answer 3

I have more problems, but that was the one that I did not understand on that assignment.

Answer 4

It's not done yet. :)

Answer 5

-2cosx/(1+cosx)sinx

Answer 6

Yup. There are other things you can do to it, but I don't necessarily think they're simplifications. Maybe you can spot some simplifications I can't thought.

Answer 7

Thanks, I'll send you a message if I get another question.

Answer 8

Ok, glad I could help.