Question

sin4x+sin2x =0
find the principal solution..??? ​

Answer 1

Step-by-step explanation:

sin 4x - sin 2x = 0

2 sin 2x cos 2x - sin 2x = 0

(2 cos 2x - 1) sin 2x = 0

Zero product property.

Case 1: 2 cos 2x - 1 = 0

cos 2x = 1/2

2x = 2kπ ± π/3 ; k ∈ Z

x = kπ ± π/6 ; k ∈ Z

Case 2: sin 2x = 0

2x = kπ ; k ∈ Z

x = kπ/2 ; k ∈ Z

Thus the full solution set is:

{kπ/2 , kπ±π/6 | k ∈ Z}

Within the 0<x<2π range, this means:

{π/6,π/2,5π/6,π,7π/6,3π/2,11π/6}