Math

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I'm only aloud to manipulate one side of the problem and the end result has to match the other side of the equation

Problem 1. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 2. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 3. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

  • Math -

    I did the first one, after fixing your typo

    http://www.jiskha.com/display.cgi?id=1351823844

  • Math -

    #2 does not work for x=30° so there is a typo, or it is not and identity.

    #3
    LS = (1+sinx)/cosx + cosx/(1+sinx)
    using LCD of cosx(1+sinx)

    = ( (1+sinx)(1+sinx) + cos^2 x)/(cosx(1+sinx) )
    = 1 + 2sinx + sin^2 x + cos^2 x)/(cosx(1+sinx) )
    = (2 + 2sinx)/(cosx(1+sinx))
    = 2(1+sinx)/(cosx(1+sinx))
    = 2/cosx
    = 2secx
    = RS

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