Question

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

Answer 1

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