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14 October, 02:00

Use an identity to solve the following equation on the interval [O, 2pi).

cos2x = sin x + 1

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  1. 14 October, 02:26
    0
    x = 0, π, 7π/6, 11π/6

    Step-by-step explanation:

    cos (2x) = sin x + 1

    Use double angle formula.

    1 - 2 sin²x = sin x + 1

    Move everything to one side.

    0 = 2 sin²x + sin x

    Factor.

    0 = sin x (2 sin x + 1)

    Solve.

    sin x = 0 or - ½

    x = 0, π, 7π/6, 11π/6
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