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Math Help - Use these equalities to derive the following trig identities.

  1. #1
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    Use these equalities to derive the following trig identities.

    (A) sin(-x) = -sinx
    (B) cos(-x) = cosx
    (C) cos(x+y) = cosx cosy + sinx siny
    (D) sin(x+y) = sinx cosy + cosx siny

    I'm stuck on the very first question:

    (a) sin²x + cos²x = 1 (use (C) and cos0 = 1)

    the answers also say to use (A) and (B).. but I dunno how that would apply. It also said to use x = y. How am I supposed to use cos0 though?

    thanks in advance for the help!
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  2. #2
    Member eXist's Avatar
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    Do you know/can you use sint = y/r and cost = x/r?
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  3. #3
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    Smile

    the answer or proof looks like:
    sin(-x)=sin(0-x)=sin0cosx-sinxcos0
    sin0=0
    hence
    sin0cosx=0
    therefore
    sin0cosx-sinxcos0=0-sinxcos0=-sinx
    since cos0=1
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