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Question

If (x+1)2x3+x=Ax+Bx+Cx2+1, then sin1(AC)=....

A
π6
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B
π4
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C
π3
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D
π2
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Solution

The correct option is D π6
(x+1)2x3+x=Ax+Bx+Cx2+1
Consider, (x+1)2x3+x
=x2+2x+1x(x2+1)=Ax+Bx+Cx2+1
x2+2x+1x(x2+1)=A(x2+1)+x(Bx+C)x(x2+1)
x2+2x+1x(x2+1)=(A+B)x2+Cx+Ax(x2+1)
x2+2x+1=(A+B)x2+Cx+A

by comparing the coefficients we get
A=1,C=2,A+B=1
sin1(AC)=sin1(12)=π6
Hence, option 'A' is correct.

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