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Question -

Show that f(x) =sin x is an increasing function on (тАУ╧А/2, ╧А/2).



Answer -

Given f (x) = sin x

тЗТ┬а

тЗТ┬аfтАЩ(x)= cos x

Now, as given x тИИ (тАУ╧А/2,╧А/2).

That is 4th┬аquadrant, where

тЗТ┬аCosx> 0

тЗТ┬аfтАЩ(x)> 0

Hence, condition for f(x) to be increasing

Thus f(x) is increasing on interval┬а(тАУ╧А/2, ╧А/2).

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