Simplification of Given Equation :

Answer: (4) 3

Explanation:-
(Sin³A + Sin 3A)/Sin A + (Cos³A – Cos 3 A)/Cos A
Formula –
Sin 3A = 3 Sin A – 4 Sin³ A & Cos 3A = 4 Cos³A – 3 Cos A

Then, put the value of Sin 3A & Cos 3A in given equation,
Therefore, (Sin³ A + 3 Sin A – 4 Sin³ A)/Sin A + (Cos³ A – 4 Cos³ A + 3 Cos A)/Cos A
= (3Sin A – 3 Sin³ A) / Sin A + (3 Cos A – 3 Cos³A)/ Cos A
= 3 Sin A (1 – Sin² A)/Sin A + 3 Cos A (1 – Cos² A)/Cos A
= 3 (1 – Sin² A) + 3 ( 1 – Cos²A)
= 3 Cos² A + 3 (1 – cos² A)
= 3 (Cos² A + 1 – Cos²A)
= 3 x 1
= 3
Then, the value of given equation is 3.

Hence, the answer is (4) 3.