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Question

If x (|x|<π) and y are the solutions of the equation 12sinx+5cosx=2y28y+21, then the value of 12cot(xy2) is

A
8
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B
12
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C
5
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D
1
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Solution

The correct option is C 5
122+5212sinx+5cosx122+52
i.e., 12sinx+5cosx[13,13]

RHS =2(y24y+4)+13=2(y2)2+13
RHS 13 and LHS 13
So, the equality holds only when LHS = RHS =13

RHS =13 when y=2
LHS =13 when 1213sinx+513cosx=1
sin(x+α)=1 where tanα=512
x=π2α

xy2=(π2α)
cot(xy2)=cot(π2α)=tanα=512
12cot(xy2)=5

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