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take @=theta
sec@+tan@=x
sec@.tan@=y
eliminate @ with proper solution
sec@tan@ = y ...........1
sec@+tan@ = x ...............2
squaring eq 2
(sec@)2 + (tan@)2 + 2sec@tan@ = x2
1+2(tan@)2+2sec@tan@ = x2 (sec2@ = 1+tan2@)
1+ 2(tan@)2 + 2y = x2 ....................3 (from eq 1)
squaring eq 1
(sec@)2(tan@)2 = y2
(1+tan2@)(tan2@) = y2 ...................4
substituting tan2@ from eq3 in eq4
( x2-2y +1)(x2-2y-1) = 4y2
(x2-2y)2 - 1 = 4y2
x4 - 4x2y = 1
this is the required relation
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