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

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Question:

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

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Answer:x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12Step-by-step explanation:sin(4x) cos x − sin x cos(4x) = √2 / 2Use angle difference formula.sin(4x − x) = √2 / 2sin(3x) = √2 / 23x = π/4 + 2kπ, 3π/4 + 2kπx = π/12 + 2kπ/3, π/4 + 2kπ/3x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12

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