Sin10°Sin50°Sin60°Sin70°=√3/16

Prove it

Open in App

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

Suggest Corrections

Similar questions

sin 10^{\circ} \cdot sin 50^{\circ} \cdot sin 60^{\circ} \cdot sin 70^{\circ}

sin 50^{\circ} - sin 70^{\circ} + sin 10^{\circ} =

sin 50^{\circ} - sin 70^{\circ} + sin 10^{\circ}

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

Join BYJU'S Learning Program