Question

已知 cos(75度+a)=1/3 求 cos(105度-a)+sin(a-105度)

Answer 1

cos(75度+a)=-cos(180-75-a)=-cos(105-a)=-1/3

cos(75度+a)=sin(90-75-a)=sin(15-a)=1/3

sin(a-15)=-1/3

cos(a-15)=±2√2/3

sin(a-105)=sin(a-15-90)=sin(a-15)cos90-cos(a-15)sin90=-cos(a-15)=±2√2/3

cos(105度-a)+sin(a-105度)=-1/3±2√2/3