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-   -   Tan(x)/sec(x) + cot(x)/csc(x) =sin(x)+cos(x) (https://www.askmehelpdesk.com/showthread.php?t=421063)

  • Dec 1, 2009, 12:17 PM
    tpolwort
    tan(x)/sec(x) + cot(x)/csc(x) =sin(x)+cos(x)
    I have a couple problems I cannot solve, please help me!

    1. tan(x)/sec(x) + cot(x)/csc(x) =sin(x)+cos(x)

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

    3. sin(x)/csc(x)-1 + sin(x)/csc(x)+1 = 2tan^2(x)

    4. sin(x)[sec(x)-csc(x)] = tan(x)-1
  • Dec 1, 2009, 01:27 PM
    Perito

    Most of these types of things can be solved if you remember these definitions and identifies:

    (1)

    (2)

    (3)

    (4)

    (5)

    In addition to those, you sometimes need to look up double-angle formulas and a few similar things.

    I'll do #1. You try the others.



    substituting from #2, #3, #4, and #5:





    qed

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