Show the function, `f(x)=(2x(sinx+tanx))/(2[(x+21pi)/pi]-41)` is symmetric about origin.

Find whether the given function is even or odd: f(x)=(x(sinx+tanx)/([x+pi/pi]-1/2); whether [] denotes the greatest integer function.

Show that the function f(x) = cos (x/2+pi/4) is periodic and find its period.

In [0,pi/2] the function f(x) = log sin x is

Show that the function f(x) = (sin3x) is strict decreasing on (0, pi/2)

If f(x)=|x|^(|sinx|) ,then f'((pi)/(4)) equals

Show that the function given by f(x) = sinx is increasing in (0,pi/2) .

Verify Rolle's Theorem for the function f(x) = cos {2(x - pi/4)} in the interval [0,pi/2]

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

The primitive of the function f(x)=(2x+1)|sin x| , when pi lt x lt 2 pi is