The maximum value of 12 sinθ − 9 si...
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The maximum value of ( 12 sin theta-9 sin ^{2} theta ) is -
(A) 3
(B) 4
(C) 5
(D) None of these

JEE/Engineering Exams
Maths
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The maximum value of 12 sinθ − 9 sin^2 θ is
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( 12 sin theta-9 sin ^{2} theta=-left((3 sin theta)^{2}-12 sin theta+4right)+4 )
( =-(3 sin theta-2)^{2}+4 )
( -1 leqslant sin theta leqslant 1 Rightarrow-3 leqslant 3 sin theta leqslant 3 )
( -5 leqslant 3 sin theta-2 leqslant 1 )
( 0 leqslant(3 sin theta-2)^{2} leqslant 25 )
( -25 leqslant-(3 sin theta-2)^{2} leqslant 0 )
( -21 leqslant-(3 sin theta-2)^{2}+4 leqslant 4 )
Marimum value ( =4 )
Ophion ( (B) )

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