Question

find the solestion.
sini 10. sin 20. sin 40 .sin 60
​

Answer 1

Answer:

sin 20°.sin 40°.sin 60°.sin 80°

=sin 20.sin 60°.sin 80°.sin 40°

=sin 20.sin 60°.1/2.[2sin 80°.sin 40°]

=sin 20°.(3^1/2)/2.(1/2)[cos 40°-cos 120°]

=(3^1/2)/4.sin 20°.[cos40°+1/2]

=(3^1/2)/4.sin 20°.cos 40°+(3^1/2)/8.sin 20°

=(3^1/2)/8.[2sin 20°.cos 40°]+(3^1/2)/8.sin 20°

=(3^1/2)/8.[sin 60°-sin 20°]+(3^1/2)/8sin 20°

=(3^1/2)/8.[sin 60°-sin 20°+sin 20°]

=(3^1/2)/8.sin 60°

=[(3^1/2)/8].[(3^1/2)/2]

=3/16 , Answer.