Question

Sin20°×sin40°×sin80°=root 3/8

Answer 1

sin(20)sin(40) = (1/2)[cos(20) - cos(60)] 
=> sin(20)sin(40)sin(80) 
= (1/2)[cos(20) - cos(60)]sin(80) 
= (1/2)[cos(20)sin(80) - cos(60)sin(80)] 
= (1/2)[(1/2)(sin(100)+sin(60)) - (1/2)(sin(140)+sin(20))] 
= (1/4)[sin(80) + sin(60) - sin(40) - sin(20)] 
= (1/4)sin(60), since sin(80) - sin(40) - sin(20) = sin(60+20) - sin(60-20) - sin(20) = 2cos(60)sin(20) - sin(20) = 0 
= (3^1/2)/8