The maximum value of 12 sin x-9 sin^2x is ???
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answer : 4
explanation : we have to find maximum value of 12sinx - 9sin²x
let sinx = p
then, 12sinx - 9sin²x = 12p - 9p²
let 12p - 9p² = y
or, 9p² - 12p + y = 0
discriminant , D = (-12)² - 4(9)y ≥ 0 for all real value of p,
144 - 36y ≥ 0
then, 144 ≥ 36y ⇒4 ≥ y
hence, maximum value of y = 4
but y = 12p - 9p²
= 12sinx - 9sin²x
so, maximum value of (12sinx - 9sin²x) = 4
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