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Math

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Im really struggling with these proving identities problems can somebody please show me how to do these? I'm only aloud to manipulate one side of the equation and it has to equal the other side of the equation at the end

Problem 1. Sinx/(cotx+1) + cosx/(tanx+1) = 1/(sinx+cosx)

Problem 2. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 3. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 4. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

  • Math - ,

    often it's easier to work with just sin and cos.

    working just on the left side, we have

    sin/(cot+1) + cos/(tan+1)
    sin/(cos/sin+1) + cos/(sin/cos+1)
    sin^2/(cos+sin) + cos^2(sin+cos)
    (sin^2 + cos^1)/(sin+cos)
    1/(sin+cos)

    ta-daaaah

  • Math - ,

    2. I think you have a typo , it should have been

    sinx + cosx + sinxtanx + cosxcotx = secx + cscx

    LS = sinx + cosx + sinx(sinx/cosx) + cosx(cosx/sinx
    using a LCD of sinxcosx
    = (sin^2x cosx + sinxcos^2x) + sin^3 x + cos^3 x)/(sinxcos)
    = (cosx(sin^2 x + cos^2 x) + sinx(sin^2 x + cos^2 x) )/(sinxcosx)
    = ( cosx (1) + sinx (1) )/(sinxcosx)
    = cosx/(sinxcosx) + sinx/(sinxcosx)
    = 1/sinx + 1/cosx
    = cscx + secx
    = RS

    try the others, following Steve's suggestion of changing all into sines and cosines

  • Math - ,

    thank you so much

  • Math - ,

    Prove 1-(sinxtanx)/(1+secx)

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