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Tricky Tricky little Identities

  1. Jan 3, 2004 #1
    My friend sent me some Trigonometric proving identity questions to practise and i am usually good at them but i havent done them for a while so i have gotten a bit rusty plus these ones to me are very difficult so i would like some assistance.
    Prove 1/1+sin + 1/1-sinx = 2secsquaredx.
    ok so left side looks hardest so i started with that and did it first. It may look confusing writing the divisions.

    1/1+sinx + 1/1-sinx
    1/1+ cosx/cotx + 1/cosx
    cotx+1/cosx + 1/cosx
    cotx+1/cosx + 1
    cscx/cosx +1
    Ok so that is where i have gotten to and it doesnt seem like i can get it to equal the right side. I think i have screwed up a step and i would like any assistance if possible. Please help
  2. jcsd
  3. Jan 3, 2004 #2
    You are making it look harder than it is... Just a 3 step problem.

    [tex]\frac{1}{1+sinx} + \frac{1}{1-sinx} = \frac{2}{cos^2(x)}[/tex]
    [tex]\frac{2}{(1+sinx)(1-sinx)} = ...[/tex]
    [tex]\frac{2}{1 - sin^2(x)} = \frac{2}{cos^2(x)} = 2sec^2(x)[/tex]
  4. Jan 3, 2004 #3
    Oh you skipped step where you make bases same but ya it works, thankyou very much.
    Last edited: Jan 3, 2004
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