Statement 1: Let `f(x)=sin(cos x)in[0,pi/2]dot` Then `f(x)` is decreasing in `[0,pi/2]` Statement 2: `cosx` is a decreasing function `AAx in [0,pi/2]`

Show that f(x)=cos^(2)x is a decreasing function on (0,pi/2)

Show that f(x)=cos^(2)x is decreasing function on (0,(pi)/(2))

Statement 1: let f(x)=2tan^(-1)((1-x)/(1+x)) on [0,1] then range of f=[0,(pi)/(2)] Statement 2:f decreases from (pi)/(4) to 0

If f(x)=sinx-cosx , the function decreasing in 0 le x le 2pi is

Statement-2 f(x)=(sin x)/(x) lt 1 for lt x lt pi/2 Statement -2 f(x)=(sin x)/(x) is decreasing function on (0,pi//2)

Prove that the function f(x)=cos x is neither increasing nor decreasing in (0,2 pi)

Let f(x)=1+2sin x+2cos^(2)x,0<=x<=(pi)/(2) then

Statement 1: Both sin xand cos x are decreasing functions in ((pi)/(2),pi) Statement 2: If a differentiable function decreases in an interval (a,b), then its derivative also decreases in (a,b).

Show that f(x)=sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi) and neither increasing nor decreasing in (0,pi)