Solve sin(2x)cos(6x)-cos(2x)sin(6x)=-0.7

Question

Solve sin(2x)cos(6x)-cos(2x)sin(6x)=-0.7

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Serenity 2 weeks 2021-09-09T15:23:53+00:00 1 Answer 0

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    2021-09-09T15:25:25+00:00

    Answer:

    x = π/4 – 1/4 sin^(-1)(7/10) + (π n_1)/2 for n_1 element Z

    or x = (π n_2)/2 + 1/4 sin^(-1)(7/10) for n_2 element Z

    Step-by-step explanation:

    Solve for x:

    cos(6 x) sin(2 x) – cos(2 x) sin(6 x) = -0.7

    -0.7 = -7/10:

    cos(6 x) sin(2 x) – cos(2 x) sin(6 x) = -7/10

    Reduce trigonometric functions:

    -sin(4 x) = -7/10

    Multiply both sides by -1:

    sin(4 x) = 7/10

    Take the inverse sine of both sides:

    4 x = π – sin^(-1)(7/10) + 2 π n_1 for n_1 element Z

    or 4 x = 2 π n_2 + sin^(-1)(7/10) for n_2 element Z

    Divide both sides by 4:

    x = π/4 – 1/4 sin^(-1)(7/10) + (π n_1)/2 for n_1 element Z

    or 4 x = 2 π n_2 + sin^(-1)(7/10) for n_2 element Z

    Divide both sides by 4:

    Answer: x = π/4 – 1/4 sin^(-1)(7/10) + (π n_1)/2 for n_1 element Z

    or x = (π n_2)/2 + 1/4 sin^(-1)(7/10) for n_2 element Z

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