证明sin(2a+b)/sina-2cos(a+b)=sinb/sina

来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/21 20:49:10
证明sin(2a+b)/sina-2cos(a+b)=sinb/sina证明sin(2a+b)/sina-2cos(a+b)=sinb/sina证明sin(2a+b)/sina-2cos(a+b)=s

证明sin(2a+b)/sina-2cos(a+b)=sinb/sina
证明sin(2a+b)/sina-2cos(a+b)=sinb/sina

证明sin(2a+b)/sina-2cos(a+b)=sinb/sina
左边=[sin(2a+b)-2cos(a+b)sina]/sina
=[sina*cos(a+b)+sin(a+b)*cosa-2cos(a+b)sina]/sina
=[sin(a+b)*cosa-cos(a+b)sina]/sina
=sin(a+b-a)/sina
=sinb/sina
=右边
所以结论成立.
逆推法：
sin(2a+b)/sina-2cos(a+b)=sinb/sina
<==>sin(a+a+b)-2cos(a+b)sina=sinb
<==>sinacos(a+b)+cosasin(a+b)-2cos(a+b)sina=sinb
<==>cosasin(a+b)-cos(a+b)sina=sinb
<==>sin(a+b-a)=sinb
<==>sinb=sinb恒成立
以上各步可逆
证毕

左=(sin(2a+b)-2cos(a+b)sina)/sina
=(sin(2a+b)-(sin(a+b+a)-sin(a+b-a)))/sina
=sinb/sina
运用了三角函数的积化和差
2cosasinb=sin(a+b)-sin(a-b)

∵sin(2a+b)-2sinacos(a+b)=sin2acosb+cos2asinb-2sina(cosacosb-sinasinb)
=2sinacosacosb+(cos²a-sin²a)sinb-2sinacosacosb+2sin²asinb
=cos²asinb-sin²asinb+2sin²asinb
=cos²asinb+sin²asinb
=(cos²a+sin²a)sinb
=sinb
∴sin(2a+b)/sina-2cos(a+b)=sinb/sina

如图

证明sina sin(a+2b) - sinb sin(b+2a) =sin(a+b)sin(a-b) 证明sin(2a+b)/sina-2cos(a+b)=sinb/sina 证明sin(2a+b)/sina-2cos(a+b)=sinb/sina 证明三角函数等式sin(A+B)-sinA=2cos(A+B/2)sin(B/2) 懂得进.证明,sina+sin(a+b)+sin(a+2b)+...sin(a+nb)=sin(a+ab/2)sin[(n+1)b/2]/sin(b/2) 证明sin^2a+sin^2β+1>sina*cosa+sina+sinβ 如何证明sinA+sinB=2sin((A+B)/2)cos((A-B)/2) 证明sin(a+b)-sina=2sinb/2*cos(a+b/2) 证明:sin(2a+b)/sinb-2cos(a+b)=sinb/sina急 sinA(cos(2A+B)+cosB)=cosA(sin(2A+B)-sinB)证明 tan(A+B)=2tanB 证明3sinA=sin(A+2B) tan(A+B)=2tanB 证明3sinA=sin(A+2B)笑嘻嘻 sinb/sina=cos(a+b),证明3sinb=sin(2a+b) 证明三角函数(和角公式)cosa(cosa-cosb)+sina(sina-sinb)=2sin²(a-b/2) 怎么证明2sinA*cosA=sin(2A) sinA+sinB-sinC=4sin(A/2)sin(B/2)cos(C/2)证明上式 用反证法证明:已知a,b都是锐角,且sin(a+b)=2sina,求证a 证明sin(a+b)sin(a-b)=(sina+sinb)(sina-sinb)