Prove It ??
Sin10°Sin50°+Sin50°Sin250°+Sin250°Sin10°=0
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"How do the valence electrons change as you go across a period?"
Not true; the expression evaluates to #–0.75#.
#sin 10° = 0.1736#
#sin 50° = 0.7660#
#sin 250° = –0.9397#
#sin 10° xx sin 50°" " = " "0.1330#
#sin 50° xx sin 250° = –0.7198#
#sin 250° xx sin 10° = –0.1632#
#=> sin 10°sin 50°+sin 50°sin 250°+sin 250°sin 10°#
#=0.1330 - 0.7198 - 0.1632#
#=–0.75#
#rarrsin10sin50+sin50sin250+sin250sin10#
#=1/2[2sin10sin50+2sin50sin250+2sin250sin10]#
#=1/2[cos(50-10)-cos(50+10)+cos(250-50)-cos(250+50)+cos(250-10)-cos(250+10)]#
#=1/2[cos40-cos60+cos200-cos300+cos240-cos260]#
#=1/2[-cos60+cos40+cos(180+20)-cos(360-60)+cos(180+60)-cos(180+80)]#
#=1/2[-cos60+cos40-cos20-cos60-cos60+cos80]#
#=1/2[-3cos60+2cos((80+40)/2)cos((80-40)/2)-cos20]#
#=1/2[-3cos60+2cos60cos20+cos20]#
#=1/2[-3*(1/2)+2*(1/2)cos20-cos20]#
#=-3/4#
