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Anônimo(a)
Asked: 2011-02-27T15:46:56-03:00

Trigonometria – Prova de identidade?

Prove a identidade:
tg²x-(1/cossec²x)+(1+2sen²xsec²x)/sec²x=sec²x
o final é: sec²x=sec²x

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  1. Warles

    Veja: algumas identidades úteis:
    tgx = senx/cosx
    cossecx = 1/senx
    sec²x = 1/cosx
    sen²x + cos²x = 1

    Logo,
    tg²x – (1/cossec²x) + (1+2sen²xsec²x)/sec²x =
    sen²x/cos²x – [1/(1/sen²x)] + 1/sec²x + (2sen²x . sec²x)/sec²x =
    sen²x/cos²x – sen²x + 1/(1/cos²x) + 2sen²x =
    sen²x/cos²x + (cos²x + sen²x) =
    sen²x/cos²x + 1 =
    (sen²x + cos²x)/cos²x =
    1/cos²x =
    sec²x.
    c.q.d

    Espero ter ajudado. Bons estudos!!!!!!!!!!!!!!!

    • 0
  2. Drika soouza

    Prove: Cos²x= 1/1+tg²x

    • 0

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