SOLUTION: trig identities- i need help proving that this identity is true
(sin2x/ 1+cos2x) * (cosx/1+cosx) = tan(x/2)
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-> SOLUTION: trig identities- i need help proving that this identity is true
(sin2x/ 1+cos2x) * (cosx/1+cosx) = tan(x/2)
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Question 147846: trig identities- i need help proving that this identity is true
(sin2x/ 1+cos2x) * (cosx/1+cosx) = tan(x/2) Found 2 solutions by vleith, Nate:Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website! Assume you have double angle and half angle identities already 'in your bag of trick'. See http://homepage.mac.com/shelleywalsh/MathArt/DoubleHalf.html
Namely
sin(2x) = 2sin(x)cos(x)
cos(2x) = 2cos^2(x)-1
tan(x/2) = sin(x)/(1+cos(x))
Now let's start at the top
(sin2x/ 1+cos2x) * (cosx/1+cosx) =
((2sin(x)cos(x)) / (1 + (2cos^2(x)-1)) * (cosx/1+cosx) =
((2sin(x)cos(x)) / (2cos^2(x)) * (cosx/1+cosx) =
((sin(x)cos^2(x)) / (cos^2(x)) * 1/(1+cosx) =
sin(x) * 1/(1+cosx) =
sin(x)/(1+cosx) =
tan(x/2)
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