If x=a sec A+ b tan A and y=a tan A+ b sec A, prove that x^2-y^2=a^2-b

1.	If x=a sec A+ b tan A and y=a tan A+ b sec A, prove that x^2-y^2=a^2-b^2
Answer» X= a secA+b tanAY= a tanA+b secAOn squaring we get the following;X2+Y2= a2 sec2A+b2 tan2A - (a2 tan2A+b2 sec2A)X2+Y2=a2 sec2A+b2 tan2A - a2- tan2A-b2-sec2AX2+Y2= a2-b2 hence proved.

Discussion