Question

maximum value of 12sinx-9 sin^2x

Answer 1

12sinx - 9sin^2x can be written as below by completing the squares method,
= 4 - ( 9sin^2x - 12sinx + 4 )
= 4 - ( 3sinx -2 )^2
= 4 - z^2
Now, the above expression will have maximum value only when z = 0.
so, maximum value is 4 and occurs when sinx = 2/3.