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If x = sec ϕ - tanϕ and y = cosec ϕ + cot ϕ then show that xy + x -y +1=0.

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If x = sec ϕ - tanϕ and y = cosec ϕ + cot ϕ then show that xy + x -y +1=0.

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We need to eliminate  2A=ϕ 

y=cosec2A+cot2A=(1+cos2A)/sin2A=cot A

x=sec2A-tan2A=(1+1/y^2)/(1-y^2)-(2/y)(1-1/y^2)=(y^2+1)(y^2-1)-2y/(y^2-1)=(y-1)/(y+1)

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