Determine whether `f(x)=-x//2+sinx` is increasing or decreasing on `(-pi//3,\ pi//3)` .

Determine whether f(x)=-x/2+sin x is increasing or decreasing on (-pi/3,pi/3)

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

Show that f(x)=sinx is an increasing function on (-pi//2,\ pi//2) .

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

Determine whether the following function is increasing or decreasing in the given interval : f(x) =cos (2x+(pi)/(4)), (3pi)/(8) le x le (5pi)/(8) .

Determine whether the following function is increasing or decreasing in the given interval : f(X) = cos (2x + (pi)/(4)), (3pi)/(8)lexle(5pi)/(8) .

Find the interval for which the function f(x) = tanx- 4 (x- 2) is increasing and decreasing in (-pi/2,pi/2) .

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

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