Can some explain to me why xcos(x) - sin(x) will = 0 when x = tan(x)?

Thanks.

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- Nov 6th 2012, 06:55 AMalyosha2x = tan(x)
Can some explain to me why xcos(x) - sin(x) will = 0 when x = tan(x)?

Thanks. - Nov 6th 2012, 06:57 AMPlatoRe: x = tan(x)
- Nov 6th 2012, 07:09 AMalyosha2Re: x = tan(x)
I understand that, but I don't see how the answer follows from this.

- Nov 6th 2012, 07:24 AMalyosha2Re: x = tan(x)
I just don't see it. why is the output of the function needed to be the same as the input? How does that help? What effect does cos or sin have on sinx/cosx? I can't seem to find a pattern. What's the releveance of having tanx * cos(tanx)? Am I thinking about it in the right way? If x and tanx are then interchangeable, what is it that is so special about the value of x at the points where x = tanx that makes it work? I've spend two hours trying to figure this out and I am just completely lost.

- Nov 6th 2012, 07:40 AMalyosha2Re: x = tan(x)
I've had an idea. Is it because x and tanx are interchangeable you can use tanx only as a replacement for the first x leaving you with sinx/cosx * cosx - sinx = sinx - sinx = 0?

- Nov 6th 2012, 04:35 PMProve ItRe: x = tan(x)
- Nov 6th 2012, 05:57 PMtopsquarkRe: x = tan(x)
- Nov 6th 2012, 06:14 PMHallsofIvyRe: x = tan(x)
- Nov 6th 2012, 07:03 PMProve ItRe: x = tan(x)
- Nov 6th 2012, 07:48 PMtopsquarkRe: x = tan(x)
@ Halls and Prove It, good point.

-Dan