Question

已知cos(75°+α)=,其中α为第三象限角．则cos(105°-α)+sin(α-105°)的值是______________．

Answer 1

答案：-

解析：∵cos(105°-α)=cos［180°-(75°+α)］=-cos(75°＋α)=-, sin(α-105°)=-sin(105°-α)=-sin［180°-(75°+α)］=-sin(75°+α),?∵cos(75°+α)=＞0,且α为第三象限角，故75°+α为第四象限角，故sin(75°+α)=-=-.故原式=--=-.