Anonymous
Anonymous asked in Social ScienceOther - Social Science · 4 months ago

Why are all these false?

1) arcsin (x) = csc (x) 

2) ln(x) - ln (y) = ln(x)/ln(y)

3) cos(2x)/2 = cos (x)

1 Answer

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  • 4 months ago

    1)

    arcsin(x) is an angle, θ, where sin(θ) = x

    csc(x) = 1/sin(x)

    For example, arcsin(1) = π ≈ 3.14,

    but csc(1) = 1/sin(1) ≈ 0.84

    Hence, arcsin(x) ≠ csc(x)

    ====

    2)

    ln(x) - ln(y) = ln(x/y) ≠ ln(x)/ln(y)

    For example, when x = 3 and y = 2:

    ln(x) - ln(y) = ln(3) - ln(2) ≈ 0.405,

    but ln(x)/ln(y) = ln(3)/ln(2) ≈ 1.58

    Hence, ln(x/y) ≠ ln(x)/ln(y)

    ====

    3)

    cos(2x)/2 = [cos²(x) - sin²(x)]/2 ≠ cos(x)

    For example, when x = 30°:

    cos(2x)/2 = cos(60°)/2 = 1/4,

    but cos(x) = cos(30°) = √3/2

    Hence, cos(2x)/2 ≠ cos(x)

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