Question

一道高三数学题,高手入!!!!!!!!!!

求证(sin$+sin2$+sin3$+sin4$)/(cos$+cos2$+cos3$+cos4$)=tan(5$/2)

HELP!

Answer 1

把楼主的$换成了a。
sina+sin2a+sin3a+sin4a
=sina+sin4a+sin2a+sin3a
=2[sin(5a/2)cos(3a/2)]+2[sin(5a/2)cos(a/2)]
=2sin(5a/2)*[cos(3a/2)+cos(a/2)]

另一方面
cosa+cos2a+cos3a+cos4a
=cosa+cos4a+cos2a+cos3a
=2[cos(5a/2)cos(3a/2)]+2[cos(5a/2)cos(a/2)]
=2cos(5a/2)*[cos(3a/2)+cos(a/2)]

(sina+sin2a+sin3a+sin4a)/(cosa+cos2a+cos3a+cos4a)
={2sin(5a/2)*[cos(3a/2)+cos(a/2)]}/{2cos(5a/2)*[cos(3a/2)+cos(a/2)]}
=tan(5a/2)

即
(sin$+sin2$+sin3$+sin4$)/(cos$+cos2$+cos3$+cos4$)=tan(5$/2)