If 2x = sec A and 2/x = tan A then

Given: 2x = sec A, and 2/x = tan A

Consider 2(x² – (1/ x²))

=

=

= (1/2) [sec² A – tan² A]

= (1/2)[1]

= 1/2 (∵ sec² x – tan² x = 1)