sin(45+α)=√5/5,则sinαcosα=

来源:学生作业帮助网 编辑:作业帮 时间:2024/08/06 03:26:03
sin(45+α)=√5/5,则sinαcosα=
x=N0V.%]DT(BP@VJ[8@$WO TX"N$Nwx]"T,fjg/͔!?YS~6tׇЄe =w'/_r׺=*FU+zj>>\"0ELwOzv>9/ČWO3H"SN۶6'}݆Qɶ$ruR.#y)Y)-ƌaN\0.zM N(Xih Y bkMfl~ Y

sin(45+α)=√5/5,则sinαcosα=
sin(45+α)=√5/5,则sinαcosα=

sin(45+α)=√5/5,则sinαcosα=
根据sin(45°-α)=5/13建立如图三角形关系.
由上图求出 cos(45°-α)=12/13
由和差角公式:
sin(45°-α)=sin45°cosα-cos45°sinα = ( √2/2)(cosα-sinα) = 5/13
cos(45°-α)=cos45°cosα +sin45°sinα=( √2/2)(cosα+sinα)=12/13
cos(45°+α)=cos45°cosα -sin45°sinα=( √2/2)(cosα-sinα)=5/13
( √2/2)(cosα-sinα) = 5/13 (1)
( √2/2)(cosα+sinα)=12/13 (2)
(1) (2)联立求解 sinα=(7√2)/26
sinα/cos(45°+α)=((7√2)/26)/(13/5)=(7√2)/10