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Show that the function f given by `f(x)=tan^(-1)(sinx+cosx),` `x" ">" "0` is always an strictly increasing function in `(0,pi/4)` .

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`f(x)=tan^(-1)(sinx+cosx)`
`f^'(x)=1/(1+sinx+cosx)^2 d/(dx)(sinx+cosx)`
`f^'(x)=1/(1+sin^2x+cos^2x+2sinxcosx) (cosx-sinx)`
`f^'(x)=(cosx-sinx)/(2+sin2x)`
Thus,
`2+sin2x` is always `gt 0`
And,
...
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