Cos (x-y) ------------ = Cos (x+y) 1 + tanx tany -------------- 1 - tanx tany and Sin 3x=3sinx-4sin^3x Any help would be greatly appreciated
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Originally Posted by mortifiedpenguin Cos (x-y) ------------ = Cos (x+y) 1 + tanx tany -------------- 1 - tanx tany Spoiler: and Sin 3x=3sinx-4sin^3x Any help would be greatly appreciated Spoiler: Continue applying identities to get everything in terms of sine and its powers. Then simplify to get the result! I hope these hints help!
I would start with and transform them into something to which you can apply the angle sum identities for cosine. (i.e. cos(x+y) = cos(x)cos(y)-sin(x)sin(y) and cos(x-y)=cos(x)cos(y)+sin(x)sin(y) )
Hello, mortifiedpenguin! We have: . Divide numerator and denominator by . .
sin 3x = sin( 2x +x ) = sin2xcosx + sinxcos2x = (2sinxcosx)cosx + (cos^2x - sin^2x)sinx = 2sinxcosx^2 + cos^2xsinx - sin^3x = ...
Last edited by Chris L T521; May 28th 2011 at 04:33 PM. Reason: edited out last part of full solution.
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