Pre-calculus

Prove the following identities.
1. 1+cosx/1-cosx = secx + 1/secx -1
2. (tanx + cotx)^2=sec^2x csc^2x
3. cos(x+y) cos(x-y)= cos^2x - sin^2y

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  1. correction for #1, should say:

    (1+cosx)/(1-cosx) = (secx + 1)/(secx - 1)

    RS = (1/cosx + 1)/(1/cosx - 1)
    = (1/cosx + 1)/(1/cosx - 1) * cosx/cox
    = (1+ cosx)/(1 - cosx)
    = LS
    Well, that was easy.

    #2, hint: change everything to sines and cosines
    expand and simplify the LS

    #3, use the expansion for cos(A ± B), multiply the result and watch what happens.
    hint: remember a^4 - b^4 = (a^2+b^2)(a^2-b^2)

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