SOLUTION: Prove that each is an identity (sin 2 x + sin x)/ (cos 2 x + cos x + 1) = tan x

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Question 443329: Prove that each is an identity
(sin 2 x + sin x)/ (cos 2 x + cos x + 1) = tan x
Answer by lwsshak3(11628) About Me  (Show Source):
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Prove that each is an identity
(sin 2 x + sin x)/ (cos 2 x + cos x + 1) = tan x
..
sin2x+sinx/cos2x+cosx+1=tanx
start with left side
2sinxcosx+sinx/cos^2x-sin^2x+cosx+1
sinx(2cosx+1)/cos^2x-1+cos^2x+cosx+1
sinx(2cosx+1)/2cos^2x+cosx
sinx(2cosx+1)/cosx(2cosx+1)
sinx/cosx=tanx
left side=right side