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

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

Prove that the function f given by f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi) .

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

Prove that the function f given by f(x) = log sin x" is increasing on "(0,pi/2) and decreasing on (pi/2,pi) .