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

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

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)=cosx is strictly decreasing in (0,\ pi)

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

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

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

Let f(x) =e^(2x) -ae^(x)+1. Prove that f(x) cannot be monotonically decreasing for AA x in R for any value of a

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

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

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