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maths - trigonometry

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I've asked about this same question before, and someone gave me the way to finish, which I understand to some extent. I need help figuring out what they did in the second step though. How they got to the third step from the second.

[sinx + tanx]/[cosx + 1] = tanx


makes sense so far, but I don't know how they got from here to the next one


or to the next


but from there I understand



  • maths - trigonometry -

    It looks like you cut-and-pasted part of my solution I gave you for this question

    I multiplied top and bottom by (cosx -1)/cosx -1) , which of course has a value of 1 and does not change the value of the Left Side.

    It is a step similar to the one we use in "rationalizing a denominator", I noticed that this would yield cos^2x -1 , which then could be replaced by the single term sin^2x

  • maths - trigonometry -

    Wow that was a tough one... It took me so long to figure out, even with your help! Thanks Reiny! :)

  • maths - trigonometry -

    Prov that 1-(sinxtanx) / 1+sec x

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