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Find the intervals in which the function...

Find the intervals in which the function `f` given by `f(x)=sinx+cosx ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0lt=x\ lt=2pi` is strictly increasing or strictly decreasing.

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The correct Answer is:
Strictly increasing in `[(0,(pi)/(4))uu((5pi)/(4),2pi)],` Strictly decreasing in `((pi)/(4),(5pi)/(4)).`
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