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Question
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Solution
\[f\left( x \right) = \sin x\]
\[f'\left( x \right) = \cos x > 0 \forall x \in \left( \frac{- \pi}{2}, \frac{\pi}{2} \right) \left[ \because \text { Cos function is positive in first and fourth quadrant } \right]\]
\[\text { So,}f\left( x \right)\text { is increasing on }\left( \frac{- \pi}{2}, \frac{\pi}{2} \right).\]
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