已知cos(75度+α)=1/3,α为第三象限角,求cos(225度+α)+sin(435度+α)的值如题求过程谢谢.

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已知cos(75度+α)=1/3,α为第三象限角,求cos(225度+α)+sin(435度+α)的值如题求过程谢谢.

已知cos(75度+α)=1/3,α为第三象限角,求cos(225度+α)+sin(435度+α)的值如题求过程谢谢.
已知cos(75度+α)=1/3,α为第三象限角,求cos(225度+α)+sin(435度+α)的值
如题求过程谢谢.

已知cos(75度+α)=1/3,α为第三象限角,求cos(225度+α)+sin(435度+α)的值如题求过程谢谢.
∵cos(75º+α)=1/3>0
α为第三象限角
∴75º+α为第四象限角
∴sin(75º+α)=-2√2/3
∴cos(225º+α)+sin(435º+α)
=cos[150º+(75º+α)]+sin[360º+(75º+α)]
=cos150ºcos(75º+α)-sin150ºsin(75º+α)+sin(75º+α)
=-√3/2*1/3-1/2*(-2√2/3)-2√2/3
=-(2√2+√3)/6