Question

Minimum value of 12sin thita - 9sin^2 thita

Answer 1

⏭️Hyy Mate Here is your Answer

↪️Rewrite the expression as :

y = -9sin?x + 12sin X

Let t = sin X

y = -9t2 + 12t

Completing squares, we have:

y = (-9t2 + 12t - 4) + 4

y = (-9t2 + 6t+ 6t - 4) + 4

y = -3t(3t -2) + 2(3t -2) + 4

y = (-3t + 2)(3t - 2) + 4

y = 4 - (3t - 2)2

Since (3t - 2)2 is a square number and is always zero or positive, the value of y will be maximum when 3t - 2 = 0 and maximum value is 4.

This occurs when t = 2/3

=> Sin X = 2/3 :-)

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