Proving Identities?

prove the following identity:

A)

(1+cosx) / (1-cosx) = (1+secx) / (secx-1)

B)

(sinx+tanx) / (cosx+1) = tanx

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    LHS

    = (1 + cos(x)) / (1 - cos(x))

    = ((1 + cos(x))/cos(x)) / ((1-cos(x))/cos(x))

    = (sec(x) + 1) / (sec(x) - 1)

    = (1 + sec(x)) / (sec(x) - 1)

    = RHS

    LHS

    = (sin(x) + tan(x)) / (cos(x) + 1)

    = (sin(x) + sin(x)/cos(x)) / (cos(x) + 1)

    = sin(x)(1 + 1/cos(x)) / (cos(x) + 1)

    = sin(x)cos(x)(1 + 1/cos(x)) / (cos(x)(cos(x) + 1))

    = sin(x)(cos(x) + 1) / (cos(x)(cos(x) + 1))

    = sin(x) / cos(x)

    = tan(x)

    = RHS

Still have questions? Get your answers by asking now.