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)
