Question

Fast solve this question
If x=a sec theta+b tan theta
And y=a tan theta+b sec theta
Then prove that x square-y square=a square-b square.

Answer 1

hey mate here is your ans

Answer 2

hence it is given that x=a sec theta+b tan theta
squaring by both we obtain
x^2 =a ^2sec ^2theta +b^2 tan^2 theta ....(1)
it is also given that
y=a tan theta+b sec theta squaring both side
y^2 = a^2 tan ^2 theta + b^2 sec^2 theta ....(2)
subtracting 1 and 2
x^2 + y^2 = a ^2sec ^2theta + b^2 tan^2 theta - a^2 tan ^2 theta - b^2 sec^2 theta
=
a^2 sec^2 theta - a^2 tan ^ 2 theta + b^2 sec^2 theta - b^2 tan^2 theta
a^2(sec^2theta-tan^2 theta) + b^2(sec^2theta-tan^2 theta)
but we know that
sec^2theta-tan^2 theta=1
so
x^2- y^2 = a^2 - b^2
hence proove it mark pls