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trig

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How do I prove these trig identities?
secx-cosx/tanx =sinx

And

1+sinx/cosx+ cox/ 1+sinx=2secx

  • trig -

    I will show you the first problem to give you an idea how to approach proving trig identities.

    Here are a few basic identities that will help:

    sinx/cosx = tanx
    secx = 1/cosx
    cos^2x + sin^2x = 1

    Let's put everything into sine and cosine form and work the left hand side:

    (secx - cosx)/tanx = sinx
    (1/cosx - cosx)/(sinx/cosx) = sinx
    (1/cosx - cosx)(cosx)/sinx = sinx
    (cosx/cosx - cos^2x)/sinx = sinx
    (1 - cos^2x)/sinx = sinx
    sin^2x/sinx = sinx
    sinx = sinx

    And there you have it!

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