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Question
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Solution
`x^2 - y^2 = (asecθ + bTanθ)^2 - (aTanθ + bSecθ)^2`
⇒ `a^2sec^2θ + b^2Tan^2θ + 2abSecθTanθ - (a^2Tan^2θ + b^2Sec^2θ + 2abSecθTanθ)`
⇒ `sec^2θ(a^2 - b^2) + Tan^2θ(b^2 - a^2) = (a^2 - b^2)[Sec^2θ - Tan^2θ]`
⇒ `(a^2 - b^2)` [Since `sec^2θ - Tan^2θ = 1`]
Hence , `x^2 - y^2 = a^2 - b^2`
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