sec^4x+sec^2xtan^2x-2tan^4x=?

Question

how do you solve for identity?

Answer 1

1 + (tanx)^2 = (secx)^2

So, (secx)^4 + (secx)^2(tanx)^2 - 2(tanx)^4

= [(secx)^2]^2 + [1 + (tanx)^2](tanx)^2 - 2(tanx)^4

= [1 + (tanx)^2]^2 + (tanx)^2 + (tanx)^4 - 2(tanx)^4

= 1 + 2(tanx)^2 + (tanx)^4 + (tanx)^2 - (tanx)^4

= 1 + 3(tanx)^2