Question

The maximum value of 12 sin x-9 sin^2x is ???​

Answer 1

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