# Simplification of Given Equation :

**Answer: (4) 3**

**Explanation:-
**(Sin

^{3}A + Sin 3A)/Sin A + (Cos

^{3}A – Cos 3 A)/Cos A

**Formula –**

Sin 3A = 3 Sin A – 4 Sin

Sin 3A = 3 Sin A – 4 Sin

^{3}A & Cos 3A = 4 Cos^{3}A – 3 Cos AThen, put the value of Sin 3A & Cos 3A in given equation,

Therefore, (Sin^{3} A + 3 Sin A – 4 Sin^{3} A)/Sin A + (Cos^{3} A – 4 Cos^{3} A + 3 Cos A)/Cos A

= (3Sin A – 3 Sin^{3} A) / Sin A + (3 Cos A – 3 Cos^{3}A)/ Cos A

= 3 Sin A (1 – Sin^{2} A)/Sin A + 3 Cos A (1 – Cos^{2} A)/Cos A

= 3 (1 – Sin^{2} A) + 3 ( 1 – Cos^{2}A)

= 3 Cos^{2} A + 3 (1 – cos^{2} A)

= 3 (Cos^{2} A + 1 – Cos^{2}A)

= 3 x 1

= 3

Then, the value of given equation is 3.

Hence, the answer is (4) 3.