求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 18:16:36
![求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]](/uploads/image/z/12532905-9-5.jpg?t=%E6%B1%82%E8%AF%81%28sina%2Bsinb%29%5E2%2B%28cosa%2Bcosb%29%5E2%3D4cos%5E2%5B%28a-b%29%2F2%5D)
x){F̼Dm g_
$@<[ #(Z#Q7IS(&H]v6lF=ۗطlX? #1f6D$
hDa4r@aF5as@~~qAb4l$oY F'!ē4P!MO'}h}Ӂ@ x!
求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]
求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]
求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]
证明:
左边=(sina)^2+(sinb)^2+2sinasinb+(cosa)^2+(cosb)^2+2cosacosb
=2+2(cosacosb+sinasinb)
=2+2cos(a-b)
=2+2{2cos^2[(a-b)/2]-1}
=4cos^2[(a-b)/2]
=右边
证毕
左边=(sin²a+cos²a)+(sin²b+cos²b)+2(cosacosb+sinasinb)
=1+1+2cos(a-b)
=2+2{2cos²[(a-b)/2]-1}
=4cos²[(a-b)/2]=右边
命题得证