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Solution for Show That F(X) = Tan X Is an Increasing Function on (−π/2, π/2) ? - CBSE (Commerce) Class 12 - Mathematics

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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 for question: Show That F(X) = Tan X Is an Increasing Function on (−π/2, π/2) ? concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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