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If x=secphi -tanphi and y="cosec" phi+c...

If `x=secphi -tanphi and y="cosec" phi+cotphi`, then show that `xy+x-y+1=0.`

A

`x=(y+1)/(y-1)`

B

`x=(y-1)/(y+1)`

C

`y=(1+x)/(1-x)`

D

`xy+x-y+1=0`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
We have `x=(1-sinphi)/(cosphi),y=(1+cosphi)/sinphi`
Multiplying, we get
`xy=((1-sinphi)(1+cosphi))/(cosphisinphi)`
`rArr xy+1=(1sinphicosphi=sinphicosphi)/(cosphisinphi)`
`=(1-sinphi+cosphi)/(cosphisinphi)`
`andx-y=((1-sinphi)sinphi-cosphi(1+cosphi))/(cosphisinphi)`
`=(sinphi-sin^2phi-cosphi-cos^2phi)/(cosphisinphi)`
`=(sinphi-cosphi-1)/(cosphisinphi)=-(xy+1)`
Thus, `xy+x-y+1=0, x=(1+x)/(1-x)`
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