PROVE THAT sin2(x+y)-sin2x-sin2y= -4sin(x+y)sin x sin y
F.4 TRIGONOMETRY
2011-03-16 3:13 am
回答 (1)
2011-03-16 3:24 am
✔ 最佳答案
sin 2(x+y) - sin2x - sin2y= sin 2(x+y) - (sin2x + sin2y)= sin 2(x+y) - 2sin(x + y) cos(x - y)= 2sin(x+y) cos(x+y) - 2sin(x + y) cos(x - y)= 2sin(x+y) [cos(x+y) - cos(x - y)]= 2sin(x+y) [(cosx cosy - sinx siny) - (cosx cosy + sinx siny)]= 2sin(x+y) (- 2 sinx siny)= - 4 sin(x+y) sinx siny
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