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Show that 8 sin 10° sin 50° sin 70° = 1.

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Show that 8 sin 10° sin 50° sin 70° = 1.

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L.H.S. = 4 (2sin 50° sin 10°) sin70°

= 4[cos(50° − 10°) − cos (50° + 10°)] sin70° 

= 2⋅(2sin70°⋅cos40°) − 4cos60° sin70° 

= 2sin70° + 2sin30° − 2sin70°

= 2sin30° = 1

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