Question

已知cos(75°+α)=,其中α∈(200°,280°),求cos(105°-α)+sin(α-105°)的值.

Answer 1

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).

由已知可知角75°+α为第四象限角,则有

sin(75°+α)==-.

则cos(105°-α)+sin(α-105°)=-+=.