My Math Forum Derive Tangent add/sub formula. Double angle

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 September 6th, 2013, 02:56 AM #1 Member   Joined: Aug 2013 Posts: 69 Thanks: 0 Derive Tangent add/sub formula. Double angle 1) How to derive tan(s+t) = tanx + tany/ 1-tanx tany tan(s-t) = tans - tant/ (1 + tans tan t) : sin(x+y)/cos(x+y) = sinxcosy+cosxsiny/cosxcosy-sinxsiny 2)How to derive the double angle formula tan2s = 2tans/1-tan^2s zen~
September 6th, 2013, 07:07 AM   #2
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Re: Derive Tangent add/sub formula. Double angle

Quote:
 Originally Posted by yogazen2013 1) How to derive tan(s+t) = tanx + tany/ 1-tanx tany tan(s-t) = tans - tant/ (1 + tans tan t) : sin(x+y)/cos(x+y) = sinxcosy+cosxsiny/cosxcosy-sinxsiny
Excellent! Now, since you want this in terms of "tan x", which has a "cos x" in the denominator, divide each term in both numerator and denominator by cos x.
(That is, divide both numerator and denominator by $cos^2 x$.)

Quote:
 2)How to derive the double angle formula tan2s = 2tans/1-tan^2s zen~
Use the previous formula with t= -s. tan(-s)= -tan(s), of course.

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