$({\RM{Given\;Sin\;}}10 \times {\rm{\;Sin\;}}30 \times {\rm{Sin\;}}50 \times {\rm{sin\;}}70)$

$(\Rightarrow \left( {\FRAC{1}{2}} \right) \times {\rm{Sin\;}}10 \times {\rm{Sin\;}}50 \times {\rm{sin\;}}70)$ (multiply and divide with 2 cos 10)

$(\Rightarrow \frac{{{\rm{\;}}2 \times {\rm{cos}}10 \times {\rm{Sin\;}}10 \times {\rm{Sin\;}}50 \times {\rm{\;sin\;}}70{\rm{\;}}}}{{\left( {2 \times 2 \times {\rm{cos}}10} \right)}})$ ? (2SINA cosA = Sin2A)

$(\Rightarrow \frac{{{\rm{\;}}\left( {{\rm{\;Sin\;}}20{\rm{\;}} \times {\rm{Sin\;}}50 \times {\rm{sin\;}}70} \right)}}{{{\rm{\;}}4{\rm{\;cos}}10}})$ (Multiply and divide with 2)

$(\Rightarrow \frac{{2 \times {\rm{Sin\;}}20 \times {\rm{\;Sin\;}}50 \times {\rm{sin\;}}\left( {90{\rm{\;}} - {\rm{\;}}20} \right)}}{{2 \times {\rm{\;}}4{\rm{\;cos}}10}} \Rightarrow {\rm{\;}}\frac{{2 \times {\rm{Sin\;}}20 \times {\rm{cos}}20 \times {\rm{Sin\;}}50}}{{8{\rm{\;cos}}10}})$

$(\Rightarrow \frac{{{\rm{Sin\;}}40{\rm{\;}} \times {\rm{Sin\;}}50}}{{8{\rm{\;cos}}10}})$ Again multiply and divide with 2.

$(\Rightarrow \frac{{\left( {2 \times \;Sin\;40\; \times Sin\;\left( {\;90\; - \;40} \right)} \right)\;}}{{2\;x\;8\;cos10}})$

$(\Rightarrow \frac{{\;2 \times Sin\;40\; \times cos40}}{{2\;x\;8\;cos\left( {\;90\; - \;80} \right)}})$