Question

[CBS
2. If x = a sec 0 +b tan 0 and y = a tan 0 + b sec 0, prove that
(x² - y²) = (a2 - b2).​

Answer 1

Here x2 = a2 sec2 θ + 2ab sec θ tan θ + b2 tan2 θ

y2 = a2 tan2 θ + 2 ab sec θ tan θ + b2 sec2 θ

⇒ x2 – y2 = a2(sec2 θ – tan2 θ) – b2 (sec2 θ – tan2 θ)

= a2 – b2 (∵ sec2 θ – tan2 θ = 1)

Hence proved.