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Question

If 3cosθ=2sinθ, then the value of 4sinθ3cosθ2sinθ+6cosθ is:

A
18
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B
13
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C
12
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D
14
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Solution

The correct option is B 13
Given that:
3cosθ=2sinθ
cosθsinθ=23
cotθ=23
Now, 4sinθ3cosθ2sinθ+6cosθ=sinθ[43cosθsinθ]sinθ[2+6cosθsinθ]
Divided and multiplied the numerator and denominator by sinθ.
=43cotθ2+6cotθ
=4(3×23)2+(6×23)
=422+4
=26
=13.
Hence, the answer is =13.

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