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30 March, 02:05

Cot^2x csc^2x + 2 csc^2x - cot^2 = 2

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Answers (1)
  1. 30 March, 02:54
    0
    x = π/2 + πk

    Step-by-step explanation:

    cot² x csc² x + 2 csc² x - cot² x = 2

    Multiply both sides by sin² x:

    cot² x + 2 - cos² x = 2 sin² x

    Add cos² x to both sides:

    cot² x + 2 = 2 sin² x + cos² x

    Pythagorean identity:

    cot² x + 2 = sin² x + 1

    Subtract 1 from both sides:

    cot² x + 1 = sin² x

    Pythagorean identity:

    csc² x = sin² x

    Multiply both sides by sin² x:

    1 = sin⁴ x

    Take the fourth root:

    sin x = ±1

    Solve for x:

    x = π/2 + 2πk, 3π/2 + 2πk

    Which simplifies to:

    x = π/2 + πk
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