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math

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simplify the following expression sin(v+x)-sin(v-x)?
Rewrite the expression as an algebraic expression in x. sin(2cos^-1x)

  • math -

    sin(v+x) = sinv*cosx + cosv*sinx
    sin(v-x) = sinv*cosx - cosv*sinx
    subtract to get
    2cosv*sinx

    sin(cos^-1 x) = √(1-x^2)
    by definition, cos(cos^-1 x) = x

    sin(2cos^-1 x) = 2sin(cos^-1 x)cos(cos^-1 x)
    = 2√(1-x^2) * x
    = 2x√(1-x^2)

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