若cos(x+y)cos(x-y)=1/3,则cos^x-sin^y=?^为平方_数学解答

若cos(x+y)cos(x-y)=1/3,则cos^x-sin^y=?^为平方

人气：468 ℃　时间：2020-04-11 10:40:31

解答

(cosxcosy-sinxsiny)(cosxcosy+sinxsiny)=1/3
cos²xcos²y-sin²xsin²y=1/3
cos²x(1-sin²y)-(1-cos²x)sin²y=1/3
cos²x-cos²xsin²y-sin²y+cos²xsin²y=1/3
cos²x-sin²y=1/3