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Show that the function f(x)=sin(2x+pi//4...

Show that the function `f(x)=sin(2x+pi//4)` is decreasing on `(3pi//8,\ 5pi//8)` .

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Verified by Experts

We have given
`f(x)=sin(2x+pi//4)`
`impliesf′(x)=2cos(2x+pi/4)`
Now,
`x in((3pi)/8,(7pi)/8)`
`implies(3pi)/8`<`x`<`(5pi)/8`
`implies(3pi)/4`<`2x`<`(5pi)/4`
`impliespi`<`2x+pi/4`<`(3pi)/2`
...
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