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Question

The maximum value of 3cosθ+5sin(θπ6) for any real value of θ is:

A
792
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B
19
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C
31
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D
34
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Solution

The correct option is B 19
Let μ=3cosθ+5sin(θπ6)
=3cosθ+5sinθ.cosπ65cosθ.sinπ6
=12cosθ+532sinθ
max μ= (12)2+(532)2
=19

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