How do you simplify #sec^4s - tan^2s = tan^4s + sec^2s#?

Question

953 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-20T12:30:00

Use the trigonometric identity:

#sec^2s = 1/cos^2s = (sin^2s+cos^2s)/cos^2s = tan^2s +1#

so, as #sec^4s = (sec^2s)^2#

the identity:

#sec^4s -tan^2s = tan^4s +sec^2s#

becomes:

#(tan^2s+1)^2 -tan^2s = tan^4s +tan^2s +1#

and expanding the power of the binomial:

#tan^4s +2tan^2s +1 -tan^2s = tan^4s +tan^2s +1#

#tan^4s +tan^2s +1 = tan^4s +tan^2s +1#

qed