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Question Number 135019 by deleteduser12 last updated on 09/Mar/21

Answered by Dwaipayan Shikari last updated on 09/Mar/21

$$sin6°sin42°sin66°sin78°$$$$=\frac{1}{4}(cos60°-cos72°)(cos36°-cos120°)$$$$=\frac{1}{4}(\frac{1}{2}-\frac{\sqrt{5}-1}{4})(\frac{\sqrt{5}+1}{4}+\frac{1}{2})=\frac{1}{4}\left(\frac{3-\sqrt{5}}{4}\right)\left(\frac{\sqrt{5}+3}{4}\right)=\frac{1}{16}=\mathrm{\Lambda }$$$$cos6°cos42°cos66°cos78°$$$$=\frac{1}{4}(cos60°+cos72°)(cos120°+cos36°)$$$$=\frac{1}{4}(\frac{1}{2}+\frac{\sqrt{5}-1}{4})(\frac{\sqrt{5}+1}{4}-\frac{1}{2})=\frac{1}{16}=\zeta$$$$\frac{\mathrm{\Lambda }}{\zeta }=1$$

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