A. math---trigonometry : comound angles

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

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)

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

(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 .