Question

if x=asec theta + btan theta and y = atan theta +bsec theta. prove that x square-y square=a square-b square

Answer 1

x=a.sec theta+b.tan theta ----------(1)
y=a.tan theta +bsec theta-----------(2)

equation (1) and (2) squaring and then subtracting from (1) to (2)

x^2-y^2=a(sec^2theta-tan^2theta) -b (sec^2theta-tan^2theta)

we know
sec^2x-tan^2x=1

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