Q.     -k<=cos{sin+ (sin²+sin²)^0.5}<=k for all values of theta.

        Prove that k={1+sin²⁽gamma)}^0.5

   

So basically we have to find the maximum value of

 

One way to solve the problem is to let and
So we want to find the maximum value of the function:

  

 

An easy job is to see that g(x) attains it's max at

 

So,  

 

edit: replace all the '' by ''.