化简sin^2x+sin^2y-sin^2xsin^2y+cos^2xcos^2y

sin²x+sin²y－sin²xsin²y＋cos²xcos²y
= (sin²x-sin²xsin²y)+sin²y+cos²xcos²y //注：交换顺序
= sin²x(1-sin²y)+sin²y+cos²xcos²y
=sin²xcos²y+cos²xcos²y+sin²y
=cos²y(sin²x+cos²x)+sin²y //注：sin²x+cos²x=1
=cos²y+sin²y
=1

Sin^2x+Sin^2y－Sin^2xSin^2y＋Cos^2xCos^2y
= Sin^2x(1－ Sin^2y)＋Sin^2y＋Cos^2x(1－ Sin^2y)
= Sin^2x＋ Sin^2x Cos^2y＋ Sin^2y＋ Cos^2x＋Cos^2x Sin^2y
=1＋Sin^2x Cos^2y＋Sin^2y(1－Cos^2x)＋Cos^2x
=1＋Sin^2x Cos^2y＋Sin^2xSin^2y＋Cos2^x
=1＋Sin^2x( Cos^2y＋Sin^2y) ＋Cos^2x
=1＋Sin^2x＋Cos^2x
=1＋1
=2

sin²x+sin²y－sin²xsin²y＋cos²xcos²y
= sin²x＋sin²y-sin²xsin²y+(1－sin²x)(1－sin²y)
= sin²x＋sin²y-sin²xsin²y＋1-sin²x-sin²y+sin²xsin²y
=1