This is an important question from the

Book- ML Aggarwal

Board- ICSE

Publication- Avichal

Chapter- Trigonometric Identities

Chapter number-18

If x – a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 – y2 = a2 – b2.

Trigonometric Identities, class 10th, chapter 18th, question no34 , ICSE board, ML aggarwal..

Given,

x =

a sec θ + b tan θ,

y = a tan θ + b sec θ

Now,

x

^{2}– y^{2}= (a sec θ + b tan θ)^{2}– (a tan θ + b sec θ)^{2}– Hence proved.