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Question

If (x+1)2x(x2+1)=Ax+Bx+Cx2+1, then Cos1(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 C π3
LHS(x+1)2x(x2+1);RHS=Ax+Bx+Cx2+1
=A(x2+1)+(Bx+C)xx(x2+1)
LHS=RHSx2+2x+1=A(x2+1)+(Bx+C)x
Comparing the co-efficients of the power of
x
co-efficient of x2
1=A+B
co efficient of x
c=2
Co-efficient of 1
1=A
cos1(AC)=cos1(1/2)=600=π/3
cos1(A/C)=π/3

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