Prove :
sin x + sin 2x
------------------------ = tan x
1+ cos x + cos 2x
A. math---trigonometry : comound angles
2006-12-15 3:28 am
回答 (4)
2006-12-15 3:47 am
✔ 最佳答案
sin x + sin 2x ------------------------
1+ cos x + cos 2x
sinx + 2sin x cos x
= -----------------------------
cos x + 2cos^2(x)
sinx(1+2cos x)
= --------------------------
cos x(1+ 2cos x)
= tan x
2006-12-15 3:46 am
sin x + sin 2x = sin x + 2sin x cos x = sin x ( 1 +2 cos x)
1+ cos x + cos 2x =1+ cos x + 2 cos^2 x -1 =cos x + 2cos^2 x = cos x (1+cos x)
Hence,
sin x + sin 2x
------------------------ = sin x / cos x = tan x
1+ cos x + cos 2x
2006-12-14 19:47:30 補充：
SORRY.......1 =cos x 2cos^2 x = cos x (1 2 cos x)
1+ cos x + cos 2x =1+ cos x + 2 cos^2 x -1 =cos x + 2cos^2 x = cos x (1+cos x)
Hence,
sin x + sin 2x
------------------------ = sin x / cos x = tan x
1+ cos x + cos 2x
2006-12-14 19:47:30 補充：
SORRY.......1 =cos x 2cos^2 x = cos x (1 2 cos x)
2006-12-15 3:43 am
L.H.S=(sin x + sin 2x)/(1 + cos x + cos 2x)
=(sin x + 2 sin x cos x)/[1 + cos x + (2 cos² x -1)]
=[sin x (2 cos x)]/[cos x (2cos x)]
=sin x / cos x
=tan x
=R.H.S
=(sin x + 2 sin x cos x)/[1 + cos x + (2 cos² x -1)]
=[sin x (2 cos x)]/[cos x (2cos x)]
=sin x / cos x
=tan x
=R.H.S
2006-12-15 3:43 am
(sinx+sin2x)/(1+cosx+cos2x)
=(sinx+2sinxcosx)/(cosx+2cos^2x)
=[2sinx(1+cosx)]/[2cosx(1+cosx)]
=tanx .
2006-12-14 19:52:24 補充：
修正:(sinx＋sin2x)/(1＋cosx＋cos2x)=(sinx＋2sinxcosx)/(cosx＋2cos^2x)=[sinx(1＋2cosx)]/[cosx(1＋2cosx)]=tanx .
=(sinx+2sinxcosx)/(cosx+2cos^2x)
=[2sinx(1+cosx)]/[2cosx(1+cosx)]
=tanx .
2006-12-14 19:52:24 補充：
修正:(sinx＋sin2x)/(1＋cosx＋cos2x)=(sinx＋2sinxcosx)/(cosx＋2cos^2x)=[sinx(1＋2cosx)]/[cosx(1＋2cosx)]=tanx .
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