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