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Rajan@2021
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If x = asecθ+btanθ and y = atanθ+bsecθ, prove that (x²-y²)=(a²-b²)

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This is the basic and exam oriented question in which we have to show that (x²-y²)=(a²-b²) using trigonometric formulas if we have given that  x = asecθ+btanθ and y = atanθ+bsecθ

Book – RS Aggarwal, Class 10, chapter 13B, question no 2.

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1 Answer

  1. Given,

    x=asecθ+btanθ
    by squaring both side
    =(asecθ+btanθ
    =sec²θ+tan²θ+2absecθtanθ               …………….1

    And,
    y=atanθ+bsecθ
    by squaring both side
    =(atanθ+bsecθ
    =tan²θ+sec²θ+2absecθtanθ               ………………….2

    subtract eq.2 from 1
    =sec²θtan²θ+tan²θsec²θ+2absecθtanθ2abtanθsecθ
    =(sec²θtan²θ)+(tan²θsec²θ)
    = (1)+(1)
    =

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