I was looking at a solution for some math problem regarding functions and in their solution they used that x < tan(x) for x ∈ (0,1] is true without giving proof for that. I was searching on other sites if someone had a similar problem as I have but couldn't find anything, so I am posting it here for someone else to help me.
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Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Jan 12 '23 at 11:17
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Your proof will depend on the tools available. The Taylor series makes it clear for $x \in (0,\frac\pi 2)$ – Henry Jan 12 '23 at 11:19
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You can use the convexity of $\tan$ or Taylor's formula – Lelouch Jan 12 '23 at 11:19
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for a geometric proof look here: https://math.stackexchange.com/questions/881668/algebraic-proof-of-tan-xx – QED Jan 12 '23 at 11:29