1. ## Identities

$tan^4k-sec^4 k=1-sec^2 k$
$(tan^2k-sec^2k)(tan^2k+sec^2k)$
$(-1)(tan^2k+sec^2k)$
$-tan^2k-sec^2k$
What do i do next?

2. Hello, purplec16!

There's a typo . . .

$\tan^4\!x-sec^4\!x \;=\;1-{\color{red}2}\sec^2\!x$
Then your work is correct . . .

$(\tan^2\!x-\sec^2\!x)(\tan^2\!x+\sec^2\!x)$

. . $\;=\;(-1)(\tan^2\!x+\sec^2\!x)$

. . $=\; -\tan^2\!x-\sec^2\!x$

. . . . $=\; -(\sec^2x - 1) - \sec^2x$

. . . . $=\;-\sec^2x + 1 - \sec^2x$

. . . . $=\;1 - 2\sec^2x$