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Prove that function given by f(x)=sin x ...

Prove that function given by f(x)=sin x is
(i) Strictly increasing in `(-(pi)/(2),(pi)/(2))`
(ii) Strictly decreasing in `((pi)/(2),(3pi)/(2))`

Text Solution

Verified by Experts

`f(x)=sinx `
then , `f'(x)=cos x `
(i) For each ` x in (-(pi)/(2),(pi)/(2))`
`cos x gt 0`
So, `f'(x) gt 0`
f(x) is strictly increasing in `(-(pi)/(2),(pi)/(2))`

(ii) For each ` x in ((pi)/(2),(3pi)/(2))`
`cos x lt 0`
So, `f'(x) lt 0`
f(x) is strictlyu decreasing in ` x in ((pi)/(2),(3pi)/(2))`
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