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## Homework Statement

I have this function:

[itex]f(x) = \frac{1}{x}-\frac{\cos{(x)}}{\sin{(x)}}[/itex]

For all [itex]x \in R[/itex] where [itex] x \neq n \pi, n \in Z [/itex]

And then I have to solve this equation f(x)=0:

[itex]f(x) = \frac{1}{x}-\frac{\cos{(x)}}{\sin{(x)}}[/itex]

Where I have to show that it has no solutions in the interval 0 < x < Pi and that it has got one solution in the interval Pi < x < 2Pi, and then I have to approximate that solution using Maple.

## Homework Equations

## The Attempt at a Solution

You get this equation:

[itex]0 = \frac{1}{x}-\frac{\cos{(x)}}{\sin{(x)}} ⇔ \frac{1}{x}=\frac{\cos{(x)}}{\sin{(x)}}[/itex]

Or you can rewrite it to:

[itex]0 = \frac{\sin{(x)}-x \cos{(x)}}{x \sin{(x)}}[/itex]

And then just show that the nominator will never be 0.

But anyhow I cannot really see how to make proper progess, so how can I solve this? And is it true that an equation with both x and sin(x) (or cos(x)) will not have an algebraic solution?