Trigonometric Identities

  1. I can, for the mort part, understand how to derive and "proof" most of my Identity work, but some of the more complex (in my feeble opinion) problems give me quite a bit of trouble.

    Can anyone explain these?

    "Use the fundamental identities to simplify to sines and cosines:
    tan(^2)x - (csc(^2)x/cot(^2)x) "
    Someone told me the answer was (-1) and I had no idea how to get that.

    and

    "Confirm the Identity:
    (sinx)/(1-cosx) + (sinx)/(1+cosx) = 2cscx"

    Any explanations would be greatly appreciated! Thanks!
     
  2. jcsd
  3. dextercioby

    dextercioby 12,314
    Science Advisor
    Homework Helper

    HINT:Use the definitions of "composite" functions (tan,cotan,sec,csc) and the fundamental identity
    [tex]\sin^{2}x+\cos^{2}x=1 [/tex]

    Daniel.
     
  4. Hurkyl

    Hurkyl 16,090
    Staff Emeritus
    Science Advisor
    Gold Member

    My usual advice is to convert everything into sines and cosines, and clear all denominators.
     
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