Question

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`

Answer 1

Correct Answer - 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)`