Question

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

Options

•  ab

• a² − b²

•  a² + b²

• a² b²

Answer 1

Given:

`x= a secθ, y=b tanθ`

So,

`b^2x^2-a^2 y^2` 

=` b^2(a secθ)^2-a^2(btan θ)^2` 

= `b^2 a^2 sec^2 θ-a^2 b^2 tan^2θ`

=` b^2 a^2 (sec^2θ-tan^2 θ)`

We know that,`

`sec^2θ-tan^2θ=1`

Therfore, 

`b^2x^2-a^2y^2=a^2b^2`