Prove It ?? Sin10°Sin50°+Sin50°Sin250°+Sin250°Sin10°=0

Question

9972 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-18T04:21:24

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#

Answer 2 · 2018-05-18T05:19:08

#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#