Question

已知cos(75°+α)=3分之1,其中α为第三象限角,求cos(105°-α)+sin(α-105°)的值

Answer 1

cos(105°-α)=-cos[180-(105°-α)]=-cos(75°+α)=-1/3

α为第三象限角,105°-α为第四象限角

sin(α-105°)=-sin(105°-α)=√（1-1/9)=2√2/3

cos(105°-α)+sin(α-105°)=(2√2-1)/3