The function `f(theta)=(sin theta)/theta` is decreasing in the interval

The function f(theta) = cos (pi sin^(3) theta) , is

The function f(theta) = cos (pi sin^(2) theta) , is

The range of the function f (theta) =(sin theta)/( theta ) + (theta)/(tan theta) , theta in (0, (pi)/(2)) is equal to :

The range of the function f (theta) =(sin theta)/( theta ) + (theta)/(tan theta) , theta in (0, (pi)/(2)) is equal to :

If Delta=|(1, sin theta, 1 ),(-sin theta, 1, sin theta),(-1 , -sin theta, 1)| then Delta lies in the interval

For theta>pi/3 , the value of f(theta)=sec^2theta+cos^2theta always lies in the interval

Prove that y=(4sin theta)/((2+sin theta))-theta is an increasing function of theta in [0, (pi)/(2)]