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

Similar Questions

Explore conceptually related problems

The function f(x) = tan^(-1) (sin x + cos x), x gt 0 is always an increasing function on the interval

Show that the function given by f (x) = e ^(2x) is increasing on R.

Show that the function given by f (x) = 3x + 17 is increasing on R.

Show that the function given by f(x) = 7x – 3 is increasing on R.

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in :

Show that the function given by f(x) = sin x is (c) neither increasing nor decreasing in (0 , pi) .

Show that the function given by f(x) = sin x is (a) strictly increasing in (0, (pi)/2) .

Show that the function defined by f(x)= sin (x^2) is a continuous function.

Examine whether the function f given by f(x)= x^2 is continuous at x= 0.

Show that the function given by f(x) = sin x is (b) strictly decreasing in ((pi)/2, pi) .