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

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

• Note that $A,B,C$ cannot all be acute angles – Henry Dec 2 '15 at 16:55

## 1 Answer

If $y=\prod(1+\cos A)=\prod(1-\cos A)$

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