Show that `f(x)=tan^(-1)(sinx+cosx)` is decreasing function on the interval `(pi/4,pi/2)dot`

Explanation

`f(x)=x^{2}-x sin x`
`
f^{prime}(x)=2 x-x cos x-sin x`

Here,

`0 lt x lt π/2`
`
Rightarrow 0 lt sin x lt 1 and 0 lt cos x lt 1`
`
Rightarrow 2 x-x cos x-sin x>0`
`
Rightarrow f^{prime}(x)>0, forall x in(0, frac{pi}{2})`

So, `f(x) `is increasing on` (0, frac{pi}{2}).`