Question

x=a(sec theta+tan theta)square y=b(sec theta-tan theta)square find x square y square the correct answer will be mrked branliest gain 40 points marked as brainliest 5 star rating and will be thanked and followed

Answer 1

Answer:

x² - y² = a² - b² if x = asecθ + btanθ & y = atanθ + bsecθ

Step-by-step explanation:

x = asecθ + btanθ

y = atanθ + bsecθ

to be proved

x² - y² = a² - b²

LHS

= x² - y²

= (x + y)(x - y)

= (asecθ + btanθ + atanθ + bsecθ)(asecθ + btanθ - atanθ - bsecθ)

= (a(secθ + tanθ) + b(secθ + tanθ))(a(secθ - tanθ) - b(secθ - tanθ))

= (a + b)(secθ + tanθ)(a - b)(secθ - tanθ)

= (a + b)(a - b)(secθ + tanθ)(secθ - tanθ)

= (a² - b²)(sec²θ - tan²θ)

= (a² - b²)1

= a² - b²

= RHS