Question

prove that Sin10×Sin50×Sin60×Sin70=(√3)/16​

Answer 1

Answer:

Given, sin10.sin50.sin60.sin70

=sin 60.sin10.sin50.sin70

= [(√3)/2]sin10sin50sin70

= [(√3)/2]sin10(cos(-20) - cos120)/2

= [(√3)/2]sin10(cos20 - cos120)/2

= [(√3)/2](sin10cos20 - sin10cos120)/2

= [(√3)/2](sin30 + sin(-10) - 2sin10cos120)/4

= [(√3)/2](sin30 + sin(-10) + sin10)/4

= [(√3)/2](1/2)/4

= (√3)/16