If x = a sec θ and y = b tan θ, then b²x²− a²y² =

Given: x = a sec θ and y = b tan θ

⇒ x² = a² sec² θ and y² = b² tan² θ ……………………(i)

To find: b²x² – a²y²

Consider b²x² – a²y² = b² a² sec² θ – a² b² tan² θ

= a² b² (sec² θ – tan² θ)

= a² b² (1) [∵ sec² θ – tan² θ = 1]

= a² b²