The function `f(x)=tan^(-1)(sinx+cosx)` 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)=tan x is an increasing function on (-pi/2,pi/2)

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 a decreasing function on the interval on (pi/4,pi/2).

Show that f(x)=cos(2x+pi/4) is an increasing function on (3 pi/8,7 pi/8)

Prove the following f(x)=tan^(-1)(sinx+cosx) is strictly decreasing function on ((pi)/(4),(pi)/(2)) .

Show that f(x)=cos(2x+(pi)/(4)) is an increasing function on (3 pi/8,7 pi/8)

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

Show that the function f(x)=cot^(-1)(sin x+cos x) is decreasing on (0,pi/4) and increasing on (pi/4,pi/2)

f(x) = cos x is strictly increasing in the interval : (a) ((pi)/(2),pi) (b) (pi,(3 pi)/(2)) (c) (0,(pi)/(2))