sin163+sin223sin253+sin313

=sin(180-17)+sin(180+43)+sin(180+73)+sin(360-47)
=sin17+(-sin43)+(-sin73)+(-sin47)
=sin17-sin43-sin73-sin47
=sin17-sin43-cos(90-73)-cos(90-47)
=sin17-sin43-cos17-cos43

似乎还是有问题
会不会是sin163*sin223+sin253*sin313？
如果是则
=sin(180-17)*sin(180+43)+sin(180+73)*sin(360-47)
=sin17*(-sin43)+(-sin73)*(-sin47)
=-sin17*sin43+sin73*sin47
=-sin17*sin43+cos(90-73)*cos(90-47)
=-sin17*sin43+cos17*cos43
=cos(17+43)
=cos60
=1/2

sin253=sin(163+90)=cos163, sin313=sin(223+90)=cos223

sin163+sin223+sin253+sin313
= sin163+cos163+sin223+cos223
= (-根号2)*(sin163*sin45+cos163*cos45+sin223*sin45+cos223*cos45)
= (-根号2)*( cos(163-45)+cos(223-45) )
= (-根号2)*(cos118+cos178)
= (-根号2)*(cos118+cos(118+60))
= (-根号2)*(cos118+(1/2)*cos118-(根号3)/2*sin118)
= (-根号2)*(3/2*cos118-(根号3)/2*cos118)
= (-根号2)*(根号3)*( (根号3)/2*cos118-1/2*sin118)
= (-根号6)*(cos30*cos118-sin30*sin118)
= (-根号6