化简 根号下（1-sinAsinB)平方-cosA平方cosB平方

（1-sinAsinB)²-cos²Acos²B

= 1 -2sinAsinB +sin²Asin²B -cos²A cos²B

=1 -2sinAsinB +sin²Asin²B -(1-sin²A)(1-sin²B)

= 1 -(1-sin²A-sin²B+sin²Asin²B) -2sinAsinB +sin²Asin²B

=sin²A +sin²B -2sinAsinB

=(sinA -sinB)²

sqrt( (1-sinAsinB)^2-(cosA)^2(cosB)^2 )
= sqrt( 1-2sinAsinB+(sinA)^2(sinB)^2-(cosA)^2(cosB)^2 )
= sqrt( 1-2sinAsinB - ((cosA)^2(cosB)^2-(sinA)^2(sinB)^2) )
= sqrt( 1-2sinAsinB - (cosAcosB+sinAsinB)(cosAcosB-sinAsinB) )
= sqrt( 1-(cos(A-B)-cos(A+B)) - cos(A-B)cos(A+B) )
= sqrt( (1-cos(A-B))(1+cos(A+B)) )
= sqrt( 2(sin((A-B)/2)))^2 * 2(cos((A+B)/2)))^2 )
= |2sin((A-B)/2))cos((A+B)/2))|
= |sinA-sinB|

(1-sinAsinB)^2-(cosAcosB)^2=1-2sinAsinB+(sinAsinB)^2-[1-(sinA)^2][1-(sinB)^2]=(sinA)^2+(sinB)^2-2sinAsinB=(sinA-sinB)^2，最后比较sinA和sinB的大小，确定符号再开方，不能比较的话，就直接开方。