PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for Show That F(X) = Tan X Is an Increasing Function on (−π/2, π/2) ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?

#### Solution

$f\left( x \right) = \tan x$

$f'\left( x \right) = \sec^2 x$

$\text { Here },$

$\frac{- \pi}{2} < x < \frac{\pi}{2}$

$\Rightarrow \sec x > 0 \left[ \because Sec \text { function is positive in first and fourth quadrant } \right]$

$\Rightarrow \sec^2 x > 0$

$\Rightarrow f'\left( x \right) > 0, \forall x \in \left( \frac{- \pi}{2}, \frac{\pi}{2} \right)$

$\text { So },f(x)\text { is increasing on } \left( \frac{- \pi}{2}, \frac{\pi}{2} \right) .$

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Solution Show That F(X) = Tan X Is an Increasing Function on (−π/2, π/2) ? Concept: Increasing and Decreasing Functions.
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