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Question

Let 2secx3tanxextan1x=A+Bx+Cx2+(A,B,C are real constants), then which of the following(s) is/are true?

A
A=0
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B
B=1
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C
A+B=1
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D
AB=1
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Solution

The correct option is D AB=1
Given : 2secx3tanxextan1x=A+Bx+Cx2+
Put x=0 on both sides,
A=2010=0
Differentiating both sides w.r.t. x,
2secxtanx3sec2xextan1x+∣ ∣2secx3tanxex11+x2∣ ∣=0+B+2Cx+
Now putting x=0 on both sides,
B=0310+2011=1
A+B=1
AB=1

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