Prove that `f(x)=tan ^(-1)(sin x + cos x ),x gt 0 ` `f(0,pi/4)` is increasing function

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

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

Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

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

The function f(x) = x^(x) , x gt 0 , is increasing on the interval

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

Find the intervals in which function f(x) = sin x-cos x, 0 lt x lt 2pi is (i) increasing, (ii) decreasing.

Find the intervals in which function f(x) = sin x-cos x, 0 lt x lt 2pi is (i) increasing, (ii) decreasing.

If f(x)=sin x + cos^(2)x , then prove that: f(x)=f(pi-x)

Prove that the function given by f(x) = cos x is(a) strictly decreasing in (0,pi) (b) strictly increasing in (pi,2pi) , and(c) neither increasing nor decreasing in (0,2pi)