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16 December, 15:17

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

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  1. 16 December, 18:41
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    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
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