Question

find the value of sin50+sin40 /sin70​

Answer 1

Answer:

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

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

sin10°=sin(90–80)°=cos80°

sin50°=sin(90–40)°=cos40°

sin70°=sin(90–20)°=cos20°

∴sin10°sin30°sin50°sin70°=cos80°sin30°=12cos40°cos20°

=12⋅cos20°cos40°cos80°=14sin20°⋅(2sin20°cos20°)cos40°cos80°

=18sin20°⋅(2sin40°cos40°)cos80°

=116sin20°⋅(2sin80°cos80°)

=116sin20°⋅(sin160°)=116sin20°⋅(sin(180−20°))

=116sin20°⋅sin20°=116

sin10°sin30°sin50°sin70°

⟹cos80°cos60°cos40°cos20°

⟹12(cos20°cos40°cos80°)

⟹12(2sin20°cos20°)cos40°cos80°2sin20°

⟹14(2sin40°cos40°)cos80°2sin20°

⟹182sin80°cos80°2sin20°

⟹116sin160°sin20°

sin(180°−θ)=sinθ

⟹sin10°sin30°sin50°sin70°=116