How to prove this trigonometric identity

1 + tan^(4)(x) = Sec^(4)(x) - 2Tan^(2)(x)

1 + tan^4(x) = 1 + tan^4(x) + 2 tan²(x) - 2 tan²(x)
  = 1 + 2 tan²(x) + tan^4(x) - 2 tan²(x)
  = (1 + tan²(x))² - 2 tan²(x)
  = (sec²(x))² - 2 tan²(x)
  = sec^4(x) - 2 tan²(x)