若sin(30°-α)=3/1,则cos(120°+α)=求详细过程和答案

Question

若sin(30°-α)=3/1,则cos(120°+α)=_______求详细过程和答案

Answer 1

答：
sin(30°-a)=1/3,cos(30°-a)=±2√2/3
cos(120°+a)
=cos[150°-(30°-a)]
=cos150°cos(30°-a)+sin150°sin(30°-a)
=(-√3/2)cos(30°-a)+(1/2)(1/3)
=±√6/3+1/6
若sin(30°-α)=3/1,则cos(120°+α)=__±√6/3+1/6_____