HELP! Write in terms of sine and cosine then simplify: (secx-cosx)/sinx?

NetherCraft 0

I cannot figure this out to save my life…the answer in the back of my textbook says it simplifies to tanx but I just can’t figure out how to get to that…

Please help!

4 Answers

  • I’m not 100% sure but this is what i get.


    =1/cosx – cosx / sinx (because secx = 1/cosx)

    = 1-cos^2x/cosx / sinx (when u obtain a common denominator)

    =sin^2x/cosxsinx (because 1-cos^2 = sin^x and therefore u can cancel out the square of sin^2x with sinx)



    hope this helped 🙂

  • sec x = 1/cos x

    Take the numerator : sec x – cos x = 1/cos x – cos x

    = ( 1-cos ^2 x)/cos x

    = sin^2 x/cos x

    divide by sin x to get sinx/cosx = tan x

  • sec = 1/cos.

    So, eqn bcom,


    Cross multiply the numerator. So,



    Simplify the rest..

  • We know sec x = 1 / cos x. So then we have

    ([1 / cos x] – cos x) / sin x

    = (1 – cos^2 x) / sin x cos x (multiplying numerator & denominator by cos x)

    = sin^2 x / sin x cos x

    = sin x / cos x

    = tan x

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