f(x) = cos x is strictly increasing in `(pi,2pi)`

f(x) = cos x is strictly decreasing in (0, pi)

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

f(x) = sin x is a strictly increasing in (0, pi/2)

f(x) = sin x is a strictly decreasing in (pi/2,pi)

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

Prove that the function 'f' given by f (x) = log sin x is strictly increasing on (0,pi/2)

Prove that f(x)="tan"x is strictly increasing in (-pi/(2),pi/(2))

Prove that f(x)="cos"x is strictly decreasing (0,pi)

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