Question

(1)已知cos(+α)=,求cos(-α)的值.

(2)已知cos(75°+α)=,其中α为第三象限角，求cos(150°-α)+sin(α-105°)的值.

Answer 1

分析：(1)(+α)+(-α)=π.(2)(75°+α)+(105°-α)=180°,这样就可以用诱导公式求解.

解：(1)cos(-α)=-cos［π-(-α)］

=-cos(+α)=.

(2)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75°+α为第四象限角.

则有sin(75°+α)=;

则cos(105°-α)+sin(α-105°)

=

=.