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

2 Answers
May 18, 2018

Not true; the expression evaluates to –0.75.

Explanation:

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

May 18, 2018

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