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Show that f(x)=cos^2x is a decreasing fu...

Show that `f(x)=cos^2x` is a decreasing function on `(0,\ pi//2)` .

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We have given `f(x)=cos^2x`
For the function must be decreasing `f′(x)<0`
`f′(x)=−sin2x`
Now, `0`<`x`<`pi/2`
`implies0`<`2x`<`pi`
`implies−sin2x`<`0`
`impliesf′(x)`<`0`
Hence f ′(x) is decreasing on `(0,pi/2)`
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