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Numerade Educator

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Problem 83 Medium Difficulty

Show that $ \tan x > x $ for $ 0 < x < \pi /2 $. [Hint: Show that $ f(x) = \tan x - x $ is increasing on $ (0, \pi /2) $.]

Answer

$\Rightarrow \tan x>x$ for $x \in\left(0, \frac{\pi}{2}\right)$

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CM

Catthie M.

June 18, 2021

Show that: tan(x-pi)= tan x

Video Transcript

he has clears the wing. You married here. So we're showing that fffx, which is equal to 10 of X minus X, is increasing on zero comma pi over too. So we have the first derivative which is equal to sequence square minus one. We see that sequence square minus one is bigger than zero for all of access between zero comma pie house. So f of X is increasing for these values. So just makes off of acts to be bigger than f of zero. So tangent minus X is bigger than zero, which makes 10 gent of acts bigger than X when x from zero. Come on, pi house.