The value of sin 10° x sin 30° x sin 50°x
sin 70° is equal to
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ANSWER:-
sin10°=sin(90–80)°=cos80°sin10°=sin(90–80)°=cos80°
sin50°=sin(90–40)°=cos40°sin50°=sin(90–40)°=cos40°
sin70°=sin(90–20)°=cos20°sin70°=sin(90–20)°=cos20°
∴sin10°sin30°sin50°sin70°=cos80°sin30°=12cos40°cos20°∴sin10°sin30°sin50°sin70°=cos80°sin30°⏟=12cos40°cos20°
=12⋅cos20°cos40°cos80°=14sin20°⋅(2sin20°cos20°)cos40°cos80°=12⋅cos20°cos40°cos80°=14sin20°⋅(2sin20°cos20°)cos40°cos80°
=18sin20°⋅(2sin40°cos40°)cos80°=18sin20°⋅(2sin40°cos40°)cos80°
=116sin20°⋅(2sin80°cos80°)=116sin20°⋅(2sin80°cos80°)
=116sin20°⋅(sin160°)=116sin20°⋅(sin(180−20°))=116sin20°⋅(sin160°)=116sin20°⋅(sin(180−20°))
=116sin20°⋅sin20°=116=116sin20°⋅sin20°=1/16
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