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State Whether F(X) = Tan X − X is Increasing Or Decreasing Its Domain ?

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Question

State whether f(x) = tan x − x is increasing or decreasing its domain ?

Sum
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Solution

\[f\left( x \right) = \tan  x - x\] 
 
\[f'\left( x \right) =  \sec^2 x - 1\] 
 
           \[ =  \tan^2 x \geqslant 0,    \forall x \in \left[ 0, 2\pi \right]\] 
\[\text { So ,f(x)is increasing in its domain }.\]
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