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Question

The maximum value of 4sin2x−12sinx+7 is.

A
25
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B
4
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C
Does not exist
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D
None of these
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Solution

The correct option is D None of these
4sin2x12sinx+7
=4(sin2x3sinx)+7
=[(sinx32)294]+7
=4(sinx32)29+7
=4(sinx32)22
We know that , 1sinx1
52sinx3212
14(sinx32)2254
14(sinx32)225
14(sinx32)2223
Hence, maximum value is 23.

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