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Trig Identity stumped

  1. Nov 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that the LHS can be changed into the RHS.
    [tex] sec^6 x-tan^6x=1+3sec^2x tan^2x[/tex]


    2. Relevant equations

    Trig identities.

    3. The attempt at a solution
    I tried factoring the LHS:
    [tex](sec^2-tan^2)(sec^4+sec^2tan^2+tan^4)[/tex]
    [tex]sec^2-tan^2=1[/tex] so that leaves me with the other thing in the parentheses. I have tried using the Pythagorean identities on sec^2 and tan^2, I have broken up the sec^4 into sec^2*sec^2.....

    I just am not getting anywhere.
    Pointers would be nice.
    CC
     
  2. jcsd
  3. Nov 27, 2008 #2
    i get the RHS le.
    try (tan²x+1)³ - tan^6 x
    then you expand.
    Cheers:smile:

    i will be offline , i shall leave the ans in the spoiler (:

    next step:
    3tan²x+3tan^4 x +1
    next:
    1+3tan²x(tan²x+1)
    Finally:
    1+3sec²tan²x
    =RHS(shown)
     
    Last edited: Nov 27, 2008
  4. Nov 29, 2008 #3
    I got it easily after the first hint. Thanks! I had been staring at it too long to see another way.
     
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