Question

已知cos(75°+α)=,其中α是第三象限角,求cos(105°-α)+sin(α-105°)的值.

Answer 1

解:∵cos(105°-α)=cos［180°-(75°+α)］

=-cos(75°+α)=-,

∴sin(α-105°)=-sin［180°-(75°+α)］=-sin(75°+α),

∵cos(75°+α)=＞0且α为第三象限角,

∴75°+α为第四象限角.

∴sin(75°+α)=-

=-=-.

∴cos(105°-α)+sin(α-105°)=--=-.