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# Show that the function given by f (x) is equal to sin x is increasing in 0 to pie by 2

3. a) Show that the function given by f (x) = $\sin x$ is  increasing in $\left ( 0 , \pi /2 \right )$

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Given f(x) = sinx
$f^{'}(x) = \cos x$
Since,     $\cos x > 0 \ for \ each \ x\ \epsilon \left ( 0,\frac{\pi}{2} \right )$
$f^{'}(x) > 0$
Hence, f(x) = sinx is strictly increasing in   $\left ( 0,\frac{\pi}{2} \right )$

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