Prove that #sec^4s - tan^2s# equals to #tan^4s + sec^2s#? Thanks in advance

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Answer 1 · 2018-03-20T05:01:20

Please refer to a Proof in the Explanation.

We have, #sec^4s-sec^2s=sec^2s(sec^2s-1)#,

#=(tan^2s+1)tan^2s, i.e., #

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

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

Answer 2 · 2018-03-20T05:02:56

#sec^4s-tan^2s#

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

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

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

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

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

#=tan^4s +2sec^2scancel(-2)-sec^2scancel(+2)#

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

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