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साबित करें कि `sin 12^(@)sin 48^(@) sin54^(@) = (1)/(8)` |
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Answer» बायाँ पक्ष `= (1)/(2) ( 2 sin 48^(@) sin 12^(@)) sin54^(@)` `= (1)/(2) ( cos 36^(@) - cos 60^(@)) cos 36^(@)` `= (1)/(2) (( sqrt(5) +1)/(4) - (1)/(2)) . ( sqrt(5) + 1)/(4)` `= (1)/(2) ((sqrt(5) -1)/(4)) . ((sqrt(5) + 1)/(4))= ( 5-1)/( 32) = (1)/( 8)` |
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