If (1−sin⁡A)(1−sin⁡B)(1−sin⁡C)=(1+sin⁡A) (1+sin⁡B)(1+sin⁡C) , then each sides is equal to

Multiply both the sides by  (1−sin⁡A)(1−sin⁡B)(1−sin⁡C) to obtain (1−sin2⁡A) (1−sin2⁡B) (1−sin2⁡C) =cos2⁡Acos2⁡Bcos2⁡C⇒(1−sin⁡A)(1−sin⁡B)(1−sin⁡C)=±cos⁡Acos⁡Bcos⁡C