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Trigonometry> Maximum value of 12sinx-9sin^2x......,......

question mark

Maximum value of 12sinx-9sin^2x......,....................... Is??......

sayak maji , 9 Years ago

Grade 11

3 Answers

Vikas TU

M = 12sinx-9sin^2x

Differentiate it w.r.t. x

dM/dx = 0 = 12cosx – 9sin2x

or

4cosx – 3sin2x = 0

2cosx – 3sinxcosx = 0

cosx(2 – 3sinx) = 0

cosx = 0 and sinx = 2/3

x = pi/2

Put pi/2 as x once and as sinx = 2/3

the value at mximum will be the answer.

Approved

Last Activity: 9 Years ago

jagdish singh singh

$\hspace{-0.58 cm}$Given $12\sin x-9\sin^2 x=3\sin x(4-3\sin x)$\\\\\\So Using $\bf{A.M\geq G.M\;,}$ We get \\\\\\$\frac{3\sin x+4-3\sin x}{2}\geq \sqrt{3\sin x\cdot (4-3\sin x)}$\\\\\\So $3\sin x\cdot (4-3\sin x)\leq 4$ and equality hold when $\sin x= \frac{2}{3}$$

Last Activity: 9 Years ago

mycroft holmes

4 – (3 sin x -2)²

This is using the theory of quadratic equations without using derivatives

Last Activity: 9 Years ago

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