Question

If x=a tan theta,y=b sec theta then find the value of y²/b²-x²/a²

Answer 1

Answer:

Given,

x = a sec θ

y = b tan θ

To Find,

The values of b²x² - a²y².

According to question,

Given, x = a sec θ

⇒ x/a = sec θ

Given, y = b tan θ

⇒ y/b = tan θ

We know that,

sec²θ - tan²θ = 1

[ Put the values ]

⇒ (x/a)² - (y/b)² = 1

⇒ x²/a² - y²/b² = 1

⇒ b²x² - a²y²/a².b² = 1

⇒ b²x² - a²y² = a².b²

Therefore,

The value of b²x² - a²y² is a².b².

For information :

Reciprocal Identities,

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ