Question

Prove that :sin10sin30sin50sin70=1/16

Answer 1

sin10*sin30*sin50*sin70 
= sin10*(1/2)*sin50*sin70 
= 1/2 * (sin10*sin50) * sin70 
= 1/4 * (2 sin10*sin50) * sin70 
= 1/4 * (cos(50-10)-cos(50+10)) * sin70 
= 1/4 * (cos40 - cos60) * sin70 
= 1/4 * (cos40-1/2) * sin70 
= 1/4 cos40 sin70 - 1/8 sin70 
= 1/8 * (2 cos40 sin70) - 1/8 sin70 
= 1/8 * (sin(70+40) + sin(70-40)) - 1/8 sin70 
= 1/8 * (sin110 + sin30) - 1/8 sin70 
= 1/8 * (sin110 + 1/2) - 1/8 sin(180-70) 
= 1/8 * sin110 + 1/16 - 1/8 sin110
= 1/8 sin 110 + 1/16 - 1/8 sin110 
= 1/16

Answer 2

=1/2sin10sin50sin70 ……… =1/4(cos40-cos60 )sin70 ………… =1/4(cos40-0.5)sin70 ……. =1/4cos40sin70-1/8sin70 .…… =1/8(sin110+sin30)-1/8sin70 ……. =1/8sin110+1/16-1/8sin70 ………. =1/8sin(180-70)+1/16-1/8sin70 ……. =1/8sin70+1/16-1/8sin70 …… =1/16