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Zikro
Lv 5
Zikro asked in Science & MathematicsMathematics · 1 decade ago

Verify that [cosh(x)^2] - [sinh(x)^2] = 1, for all x?

I'm given a unit hyperbola (x^2 - y^2 = 1). For any value a, show that the point (x,y) = [cosh(a), sinh(a)] is on the unit hyperbola. There is a hint provided which is the question title: "Verify that [cosh(x)^2] - [sinh(x)^2] = 1, for all x."

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  • henry_yang67
    Lv 6
    1 decade ago
    Favorite Answer

    cosh(x) =( e^x + e^-x )/ 2 sinh(x) = (e^x - e^-x)/2

    when you square both, you get cosh^2 = (e^2x + e^-2x)/4 + 1/2

    sinh(x) = (e^2x + e^-2x)/4 - 1/2

    so you have the difference to be equal to 1

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