Can the Intermediate Value Theorem Prove the Infinite Roots of tan x - x = 0?

[transgalactic]

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[Gib Z]

You have to show us some work!

Basically what I understand is that you want to show that tan x -x = 0 has an infinite number of roots using the Intermediate Value Theorem. Basically, what they are doing is taking advantage of the pi-periodicity of the tangent function. To roughly understand it - within every period, x only goes through a range of pi, while the tan function goes through a range from -infinity to +infinity. Hence, it is easy to find values of x for which tan x - x is positive, and easy to find it when its negative as well.

Try putting those ideas into equations.