证明sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((x+y)/2)sin((x+

来源：学生作业帮编辑：作业帮分类：综合作业时间：2024/05/15 07:05:40

证明sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((x+y)/2)sin((x+y)/2)

sinx+siny+sinz-sin(x+y+z)=4sin[(x+y)/2]sin[(x+z)/2]sin[(y+z)/2]
sinx+siny+sinz-sin(x+y+z)
=2sin[(x+y)/2]cos[(x-y)/2]+sinz-sin(x+y)cosz-sinzcos(x+y)
=2sin[(x+y)/2]cos[(x-y)/2]+sinz[1-cos(x+y)]-sin(x+y)cosz
=2sin[(x+y)/2]cos[(x-y)/2]+2sinz*sin[(x+y)/2]^2-2sin[(x+y)/2]cos[(x+y)/2]cosz
=2sin[(x+y)/2]*{cos[(x-y)/2]+sinzsin[(x+y)/2]-cos[(x+y)/2]cosz}
=2sin[(x+y)/2]*{cos[(x-y)/2]-cos[z+(x+y)/2]}
=2sin[(x+y)/2]*2sin[(x+z)/2]sin[(y+z)/2]
=4sin[(x+y)/2]sin[(x+z)/2]sin[(y+z)/2]

证明sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((x+y)/2)sin((x+ 三角不等式证明证明sin(x+y)+sin(y+z)+sin(z+x)>sinx+siny+sinz+sin(x+y+z 已知x,y,z属于(0,派/2),sin^2x+sin^2y+sin^2z=1,求(sinx+siny+sinz)/(c 证明sin(x+y)sin(x-y)=sinx-siny 证明sin(x+y)sin(x-y)=（sinx）^2-(siny）^2. 将sinx+siny+sinz-sin(x+y+z)化为积的形式证明 [sin(2x+y)/sinx]-2cos(x+y)=siny/sinx 求函数z=sinx+siny+sin(x+y)(0 请问,如何证明sinx+siny=2*sin(x+y/2)*cos(x-y/2) 证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin(x-y)/2 将sinx＋siny＋sinz－sin（x＋y＋z）化为积的形式求证：sin(2x+y)/sinx-2cos(x+y)=siny/sinx