Prove that `f(x)=(sinx)/x` is monotonically decreasing in `[0,pi/2]dot` Hence, prove that `(2x)/pi

prove that the function f(x)=(lnx)/x , is strictly decreasing in (e ,oo)dot Hence, prove that 303^(202)<202^(303)dot

Prove that the function f(x)=cos x is strictly decreasing in (0,pi)

If g(x) is monotonically increasing and f(x) is monotonically decreasing for x R and if (gof) (x) is defined for x e R, then prove that (gof)(x) will be monotonically decreasing function. Hence prove that (gof) (x +1)leq (gof) (x-1).

Prove that the function f(x)=cos^(2)x is strictly decreasing in (0,(pi)/(2))

Show that f(x) = (x)/(sinx) is increasing on [0, (pi)/(2)]

Prove that the function f(x)=cos x is strictly increasing in (pi,2 pi)

Prove that the function f(x)=tan x-4x is strictly decreasing on (-pi/3,pi/3)

Prove that f(x)=sin x is continuous at x=(pi)/(2)

prove that cos^-1(sinx)= pi/2-x

Show that f(x)=log sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi).