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)` .

Explanation

to prove `f(x)=tan^(-1)(sinx+cosx),``x > 0`is always an strictly increasing function in `(0,pi/4)`


`f'(x)`=`1/(1+(sin(x)+cos(x))^2)xxd/dx(sin(x)+cos(x))`


`f'(x)=1/(1+sin^2(x)+cos^2(x)+2sin(x)cos(x))xx(cos(x)-sin(x))`


`(cosx-sinx)/(2+sin2x)`


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