The function `f(x)=tan^(-1) (sin x+ cos x)` is an increasing function in `(-pi/2, pi/k)`, then find k.

Show that f(x)=tan^(-1)(sin x + cos x) is an increasing function in (0, (pi)/(4)) .

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

Show that f(x)=sin x-cos x is an increasing function on (-pi/4,pi/4)

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (1)((pi)/(4),(pi)/(2))(2)(-(pi)/(2),(pi)/(4))(3)(0,(pi)/(2))(4)(-(pi)/(2),(pi)/(2))^(((pi)/(4)),(pi)/(2))^(((pi)/(4)))(2)

Show that f(x)=tan^(-1)(sin x+cos x) is an increasing function on the interval (0,pi/4)

Show that f(x)=tan^(-1)(sin x+cos x) is a decreasing function on the interval on (pi/4,pi/2).

Show that the function fgivenbyf(x)=tan^(-1)(sin x+cos x)x>0 is always an strictly increasing function in (0,(pi)/(4))

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)) .

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)) .