Prove that sin10+sin 30+sin 50+sin 70 =root3÷16

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Solution

=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

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