Question

If x=a sectheta and y= b tan theta then find b^2x^2-a^2y^2

Answer 1

Answer :

Given that,
x = a secθ and y = b tanθ

Now, b²x² - a²y²

= b²(a secθ)² - a²(b tanθ)²

= b²(a² sec²θ) - a²(b² tan²θ)

= a²b² sec²θ - a²b² tan²θ

= a²b² (sec²θ - tan²θ)

= a²b² [∵ sec²θ - tan²θ = 1]

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