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Question

If x=secϕtanϕ and y=cosecϕ+ cotϕ, then

A
x=y+1y1
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B
x=y1y+1
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C
y=1+x1x
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D
xy+xy+1=0
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Solution

The correct options are
B x=y1y+1
C xy+xy+1=0
D y=1+x1x
x=secϕtanϕx=1sinϕcosϕ=1cos(π2ϕ)sin(π2ϕ)x=2sin2(π4ϕ2)2sin(π4ϕ2)cos(π4ϕ2)
x=tan(π4ϕ2)=1tanϕ21+tanϕ2 ...(1)
y=cscϕ+cotϕ=1+cosϕsinϕy=2cos2ϕ22sinϕ2cosϕ2
y=cotϕ2 ...(2)
From (1) & (2)
x=y1y+1
xy+xy+1=0
y=x+1x1
Ans: B,C,D

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