cos(a + b)cos(a - b)
= (cosacosb - sinasinb)(cosacosb + sinasinb)
= cos²acos²b - sin²asin²b
= cos²a - cos²asin²b - sin²a + cos²asin²b
= cos²a - sin²b
= 1/3
cos(a+b)cos(a-b)=1/3
积化和差得:
1/2{[cos[(a+b)+(a-b)]+cos[(a+b)-(a-b)]}=1/3
cos2a+cos2b=2/3
2cos^2a-1+1-2sin^2b=2/3
cos^2a-sin^2b=1/3