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Question

If 1x(x2+a2)=Ax+Bx+Cx2+a2, then tan1(AB)=

A
3π4
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B
π4
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C
π4
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D
π3
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Solution

The correct option is C π4
LHS=1x(x2+a2);RHS=Ax+Bx+Cx2+a2
=A(x2+a2)+(Bx+C)x(x2+a2)x
LHS=RHS1=A(x2+a2)+(Bx+C)x
comparing the co-efficients of powers of x
co-efficients of x2
o=A+B
co-efficients of x
C=o
Co-efficient of 1
Aa2=1
A=1/a2
A=B
A/B=1
Tan1(AB)=
=Tan1(1)
=π/4
Tan1(AB)=π/4

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