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Question

If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.

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Solution

Let fx=12sinx -9 sin2x =-9sin2x-12 sin x = -3sin x2-2.3 sin x.2+22-4 =-3 sinx-22-4 =4-3 sinx-22Minimum value of 3 sinx-22 is 0.Therefore, maximum value of fx= 4-3 sinx-22 is 4.We are given that 12sinx -9 sin2x will attain its maximum value at x=α. 12sinα -9 sin2α =4-9sin2α+12sinα-4=09sin2α-12 sinα+4=09sin2α-6sinα-6sinα+4=03sinα3sinα-2-23sinα-2=03sinα-23sinα-2=0 sinα=23

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