计算:sin^a的平方+sin^b的平方-(sin^asin^b)的平方+(cos^acosa^b)的平方

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计算:sin^a的平方+sin^b的平方-(sin^asin^b)的平方+(cos^acosa^b)的平方
计算:sin^a的平方+sin^b的平方-(sin^asin^b)的平方+(cos^acosa^b)的平方

计算:sin^a的平方+sin^b的平方-(sin^asin^b)的平方+(cos^acosa^b)的平方
(sina)^2+(sinb)^2-(sinasinb)^2+(cosacosb)^2
=(sina)^2+(sinb)^2-(sinasinb)^2+[1-(sina)^2][1-(sinb)^2]
=(sina)^2+(sinb)^2-(sinasinb)^2+1-(sina)^2-(sinb)^2+(sinasinb)^2
=1

sin²a-(sinasinb)²=sin²a(1-sin²b)=sin²acos²b
sin²acos²b+(cosacosb)²=cos²b
cos²b+sin²b=1

sin²a+cos²b-(sin²asin²b)²+(cos²acos²b)²
=sin²a+cos²b+(cosacosb+sinasinb)(cosacosb-sinasinb)
=1-(1/2)[cos2a+cos2b]+cos(a+b)cos(a-b)
=1-cos(a+b)cos(a-b)+cos(a+b)cos(a-b)
=1

1