Question

if x=sec A +tan A ;y =sec A - tan A then find xy

Answer 1

XY = (secA+tanA)(secA-tanA)
XY= (secA - tanA)2

Answer 2

Answer: The value of xy is 1.

Step-by-step explanation:

Since we have given that

$x=\sec A+\tan A--------(1)\\\\y=\sec A-\tan A----------(2)$

Multiplying (1) and (2), we get that

$(\sec A-\tan A)(\sec A+\tan A)=xy\\\\\sec^2 A-\tan^2 A=xy\\\\\text{ As we know that }\sec^2 A-\tan^2 A=1\\\\1=xy$

Hence, the value of xy is 1.