Question

(secX+1)( secX-1)=(tan^2)X
help me prove this using identies

Answer 1

(a-b)(a+b)= a^2 - b^2 is an identity
So: (secx - 1)(secx + 1) = sec^2(x) - 1
= 1/cos^2(x) - 1
= 1/cos^2(x) - cos^2(x)/cos^2(x)
= [1 - cos^2(x)]/cos^2(x)
= sin^2(x)/cos^2(x)
= tan^2(x)