Question

#sin 10° sin 30° sin 50 °sin 60°=1/16
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Answer 1

How can you prove that sin 10° sin 30° sin 50° sin 70° = 1/16?

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19 Answers



Ragu Rajagopalan, Passionate Maths solver ;Reviving knowledge after 3 decades

Answered June 7, 2019 · Author has 4.6K answers and 2M answer views

How can you prove that sin 10° sin 30° sin 50° sin 70° = 1/16?

sin10°=sin(90–80)°=cos80°sin⁡10°=sin⁡(90–80)°=cos⁡80°

sin50°=sin(90–40)°=cos40°sin⁡50°=sin⁡(90–40)°=cos⁡40°

sin70°=sin(90–20)°=cos20°sin⁡70°=sin⁡(90–20)°=cos⁡20°

∴sin10°sin30°sin50°sin70°=cos80°sin30°=12cos40°cos20°∴sin⁡10°sin⁡30°sin⁡50°sin⁡70°=cos⁡80°sin⁡30°⏟=12cos⁡40°cos⁡20°

=12⋅cos20°cos40°cos80°=14sin20°⋅(2sin20°cos20°)cos40°cos80°=12⋅cos⁡20°cos⁡40°cos⁡80°=14sin⁡20°⋅(2sin⁡20°cos⁡20°)cos⁡40°cos⁡80°

=18sin20°⋅(2sin40°cos40°)cos80°=18sin⁡20°⋅(2sin⁡40°cos⁡40°)cos⁡80°

Answer 2

Answer:

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