Đề bài
Chứng minh rằng
cos2(x−a)+sin2(x−b)cos2(x−a)+sin2(x−b)−2cos(x−a)sin(x−b)sin(a−b)−2cos(x−a)sin(x−b)sin(a−b)=cos2(a−b)=cos2(a−b)
Lời giải chi tiết
Ta có:
cos2(x−a)+sin2(x−b)=1+cos2(x−a)2+1−cos2(x−b)2=1+12[cos2(x−a)−cos2(x−b)]=1+12.(−2)sin(2x−a−b)sin(b−a)=1−sin(2x−a−b)sin(b−a)=1+sin(2x−a−b)sin(a−b)
Do đó
