Question

If x=a sec theta +b tan theta and y =a tan theta +b sec theta then show that x^2-y^2= a^2-b^2​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given that,

x=asecθ+btanθ

y=atanθ+bsecθ

LHS

x

2

−y

2

=(asecθ+btanθ)

2

−(atanθ+bsecθ)

2

=a

2

sec

2

θ+b

2

tanθ+2absecθtanθ−a

2

tan

2

θ−b

2

sec

2

θ−2abtanθsecθ

=a

2

sec

2

θ+b

2

tanθ−a

2

tan

2

θ−b

2

sec

2

θ

=a

2

sec

2

θ−a

2

tan

2

θ+b

2

tanθ−b

2

sec

2

θ

=a

2

(sec

2

θ−tan

2

θ)+b

2

(sec

2

θ−tan

2

θ)

=(sec

2

θ−tan

2

θ)(a

2

−b

2

)

=1×(a

2

−b

2

)

=(a

2

−b

2

)