Question

tan^4(x)-sec^4(x)= 1 - 2ssec^2(x)

Answer 1

\[= (-1)(2\sec^2x - 1) = 1 - 2\sec^2x\]\[= (\tan^2x - \sec^2x)(\tan^2x + \sec^2x) = (\sec^2x - 1 - \sec^2x)(\sec^2x - 1 + \sec^2x)\]

Answer 2

sorry for the mess + lag :

= (tan^2x - sec^2x)(tan^2x + sec^2x)
= ( sec^2x - 1 - sec^2x)(sec^2x -1 + sec^2x)
= (-1)(2sec^2x -1)
= 1 - 2sec^2x

hence: sec^2x - tan^2x = 1

Answer 3

\[x=n \pi \pm \pi/3\]