Trig!

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The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=sin(a)cos(b)-cos(a)sin(b) are occasionally useful. Justify them. One method is to use rotation matricies. Another method is to use the established identities for cos(a+b) and sin (a+b).

  • Trig! -

    Sounds like a good justification to me. Oh, did you mean prove them? In that case, using the identities,

    cos(a-b) = cos(a + (-b)) = cos(a) cos(-b) - sin(a) sin(-b)
    = cos(a)cos(b) + sin(a) sin(b)

    sin(a-b) = sin(a + (-b)) = sin(a) cos(-b) + cos(a) sin(-b)
    = sin(a) cos(b) - cos(a) sin(b)

  • Trig! -

    Sin2x

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