Question

find maximum value of 12 sinA - 9 sin^2A.​

Answer 1

Answer:

12sinx−9sin²x

=4–4+12sinx−9sin²x

=4−(4–12\sinx+9sin²x)

=4−(2–3sinx)²

So, it takes the maximum value when

(2–3\sinx)² gives the minimum value

Since for any real value of x,the term (2–3sinx)² is always positive.

So minimum value when,

2–3\sinx=0

Or \sinx=$\frac{2}{3}$..

And the the maximum value of the given function is 4.

Answer 2

Answer:

12sinx−9sin²x

=4–4+12sinx−9sin²x

=4−(4–12\sinx+9sin²x)

=4−(2–3sinx)²

So, it takes the maximum value when

(2–3\sinx)² gives the minimum value

Since for any real value of x,the term (2–3sinx)² is always positive.

So minimum value when,

2–3\sinx=0

Or \sinx=\frac{2}{3}

3

2

..

And the the maximum value of the given function is 4.