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Prove (1+secx)/(tanx+sinx)=cscx

  • trig -

    Let's use a few identities:

    secx = 1/cosx
    tanx = sinx/cosx
    cscx = 1/sinx

    Therefore:

    (1 + 1/cosx)
    ------------ = cscx
    (sinx/cosx + sinx)

    Change 1 in the numerator to cosx/cosx, which is the equivalent of 1. Also, multiply sinx in the denominator by cosx/cosx.

    (cosx/cosx + 1/cosx)
    -------------------- = cscx
    (sinx/cosx + sinx(cosx)/cosx)

    (cosx + 1)/cosx
    ---------------- = cscx
    [sinx + sinx(cosx)]/cosx

    (cosx + 1)/[sinx + sinx(cosx)] = cscx

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

    1/sinx = cscx

    cscx = cscx

    I hope this helps.

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