Question

Sin20. Sin40. Sin60. Sin80=3/16

Answer 1

sin20. sin 40. sin60. sin80 

=> sin60[sin20.sin40.sin80] 

=>√3/2[sin20.sin(60-20).sin(60+20)] 

=>√3/2[sin 3(20)/4] 

=>√3/2[sin 60/4] 

=>√3/2[√3/2*4] 

=>√3/2*√3/8 

=3/16 
 
hope it's help u

Answer 2

LHS = sin20 . sin40 . √3/2 .sin80 

= √3/4 . sin20(2sin40.sin80)

= √3/4 . sin20(cos40 - cos120) 

= √3/4 . sin20(cos40+1/2)

= √3/8 . sin20(2cos40+1)

= √3/8 .(2cos40.sin20 + sin20)

= √3/8 . (sin60 - sin20 + sin20) 

= √3/8 .sin60

= √3/8 . √3/2

= 3/16 = RHS