<s>[INST] Find the maximum value of $(12\sin x-9\sin^{2} x)$ 
The maximum value of $(12\sin x-9\sin^{2} x)$
  is equal to 
$a.)\ 3 \\
\color{green}{b.)\ 4}  \\
c.)\ 5 \\
d.)\ \text{none of these}$

As 
$-1\leq \sin x\leq 1 ,\\
12\sin x-9\sin^{2} x \\
=12-9=3 \\
$
But the answer given is $4.$
I am looking for a short and simple way.
I have studied maths up to $12$th grade.
Note : I can't use calculus.
 [/INST] Hint: If you complete the square, you will get: 
$$12\sin x - 9\sin^2 x$$ 
$$= 4-4 + 12\sin x - 9\sin^2 x $$
$$= 4-2^2 + 2 \cdot 2 \cdot 3\sin x - (3\sin x)^2 $$
$$= 4-(3\sin x - 2)^2.$$
Now, it is easy to determine the maximum value of this expression.
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