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take @=theta sec@+tan@=x sec@.tan@=y eliminate @ with proper solution

take @=theta


sec@+tan@=x


sec@.tan@=y


eliminate @ with proper solution

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

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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