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7. sin36° sin72° sin108° sin144 is equal to |
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Answer» sin36° sin72° sin108° sin144°=sin36° sin72°sin(90° + 18°) sin(90° + 54°)=sin36° sin72°cos18° cos 54°= sin236° sin272° {since, cos18° = sin72° and cos54° = sin36°}= { ( √(10 - 2√5 ) / 4 }2[ { √(10 + 2√5) } / 4 ]2{since, sin36° = ( √(10 - 2√5 ) / 4 and sin72° = { √(10 + 2√5) } / 4} = [ (10 - 2√5 ) / 16 ] [ (10 + 2√5) } / 16 ]= { (10)2- (2√5)2} / ( 16 * 16 ) {since, (A - B)(A + B) = A2- B2}= (100 - 20) / 256= 80 / 256= 5 / 16 |
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