Question

已知cos(75°+α)= ,其中α为第三象限角,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(105°-α)=-sin［180°-(75°+α)］=-sin(75°+α).

∵cos(75°+α)=＞0,又α为第三象限角,可知角75°+α为第四象限角,

则有sin(75°+α)=

=

∴cos(105°-α)+sin(α-105°)

=