Posted by Anonymous on Thursday, July 12, 2012 at 11:34am.
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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