Question

Eliminate θ from x = a (sec θ + tan θ); y = b(sec θ - tan θ)

Answer 1

Please see the attachment

Answer 2

Answer:

After elimination of θ,equations become like this expression

xy=ab

Step-by-step explanation:

To eliminate θ from x = a (sec θ + tan θ); y = b(sec θ - tan θ)

we have to use some trigonometric identities

x = a (sec θ + tan θ)

x/a =  (sec θ + tan θ)----eq1

y = b(sec θ - tan θ)

y/b= (sec θ - tan θ)----eq2

Multiply eq 1 and 2

x/a.y/b=(sec θ + tan θ)(sec θ -tan θ)              ∴(a-b)(a+b)=a²-b²

xy/ab = sec²θ-tan²θ

xy/ab =1                        ∴ sec²θ-tan²θ =1

So,xy=ab

Thus by this way we can eliminate θ .