Solve sin4x cosx-sinx cos4x = sqrt (2) / 2 for [0, 2pi)

x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12

Step-by-step explanation:

sin (4x) cos x - sin x cos (4x) = √2 / 2

Use angle difference formula.

sin (4x - x) = √2 / 2

sin (3x) = √2 / 2

3x = π/4 + 2kπ, 3π/4 + 2kπ

x = π/12 + 2kπ/3, π/4 + 2kπ/3

x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12