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The value of sin36∘sin72∘sin108∘sin144∘ is equal to |
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Answer» => sin 36 * sin 72 * sin 108 * sin 144 => sin 36 * sin 72 * sin (180 - 72) * sin (180 - 36) => sin 36 * sin 72 * sin 72 * sin 36 => [sin 36 * sin 72]² =>¼ [ 2sin 36 * sin 72]² =>¼ [ COS 36 - cos 108]² 2sin(A)*sin(B) = [cos(A-B) - cos(A+B)] =>¼ [ cos 36 + sin 18]² ; cos(108) = cos(90+18) = -sin(18)] =>¼ [ (√5 + 1)/4 + (√5 - 1)/4]² ; PUT cos 36 = (√5 + 1)/4 and sin 18 = (√5 - 1)/4 =>¼ [ √5/2 ]² => 5/16 |
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