cos (A + B) sin (C – D) = cos (A – B) sin (C + D)

(To make the math easier, while expanding this out I’ll use c A instead of cos A and s A instead of sin A)

⇒ (c A c B – s A s B)(s C c D – c C s D) = (c A c B + s A s B)(s C c D + c C s D)

⇒ c A c B s C c D – c A c B c C s D – s A s B s C c D + s A s B c C s D = c A c B s C c D +

c A c B c C s D + s A s B s C c D + s A s B c C s D

⇒ 2s A s B s C c D = -2c A c B c C s D

⇒ sin A sin B sin C cos D = -cos A cos B cos C sin D

⇒ tan A tan B tan C = - tan D (Ans)