Prove that sin 10° . sin50°. sin 70° = 1/8
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Step-by-step explanation:
LHS=sin10°sin50°sin70°.
=sin10° cos(90∘−50°)cos(90∘−70°).
=2sin10∘cos10∘cos40∘cos20∘/2cos10
=2sin20∘cos20∘cos40/4 cos10
=2sin40∘cos40/8cos10∘.
=sin80/8cos10∘
=cos10/8cos10
=1/8.
Hence proved
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