Question

sin10sin50+sin50sin250+sin250sin10=-3/4

Answer 1

sin10sin50+sin50sin250+sin250sin10=-3/4

=1/2(2sin10sin50+sin50sin250+sin250sin10)

=1/2(cos40-cos60+cos200-cos300+cos240-cos260)

=1/2(-cos60cos40+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*1/2COS20-COS20)

=-3/4