[" 32.show that the function "f" given by "f(x)=tan^(-1)(sin x+cos x)" is decreasing for all "],[quad x varepsilon(pi/4,pi/2).]

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Show that the function f given by f(x)=tan^(-1)(sin x + cos x), x gt 0 is always an increasing function in (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 given by f(x) = sin x is (b) strictly decreasing in ((pi)/2, pi) .

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

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)

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)) .