Answer:
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
