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If $$(1+ \cos A) (1+ \cos B) (1+\cos C)= y = (1- \cos A) (1-\cos B) (1-\cos C)$$ then prove that $$y = \pm \sin A \sin B \sin C$$

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  • $\begingroup$ Note that $A,B,C$ cannot all be acute angles $\endgroup$ – Henry Dec 2 '15 at 16:55
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If $y=\prod(1+\cos A)=\prod(1-\cos A)$

$y^2=y\cdot y=\prod(1+\cos A)\cdot\prod(1-\cos A)=\prod(1-\cos A)(1+\cos A)=\cdots$

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