Show that the function `f(x)=sin^(4) x+ cos^(4) x`
(i) is decreasing in the interval`[0,pi/4]`.
(ii) is increasing in the interval `[pi/4,pi/2]`.

Show that the function f(x) = log (sin x) (i) is strictly increasing in the interval ]0,pi/2[ . (ii) is strictly decreasing in the interval ]pi/2,pi[ .

Show that the function f(x) =sin^(4)x+cos^(4)x is increasing in (pi)/(4) lt x lt (3pi)/(8) .

Show that the function f(x)=sin(2x+pi/4) is decreasing on (3 pi/8,5 pi/8)

Show that the function f(x) = log cos x is : (i) Strictly decreasing in ]0,pi/2[ (ii) Strictly increasing in ]pi/2, pi [

The function f(x)= cos ((pi)/(x)) is decreasing in the interval

The function f(x)=cos((pi)/(x)),(x!=0) is increasing in the interval

Show that the function f(x)=sin(2x+pi//4) is decreasing on (3pi//8,\ 5pi//8) .

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