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# Eliminating parameter to find cartesian equation watch

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1. I'm trying to eliminate the paramter to find a cartesian equation. The problem given is

x=cosh t
y=sinh t

The answer sections gives x2-y2=cosh2t-sinh2t. Then it says t=1. How did it get to t=1? I understand the first part, both sides were squared. Many thanks
2. x = cosht, y = sinht
x^2 - y^2 = cosh^2(t) - sinh^2(t) = 1

3. Is that something I'm just supposed to know? I've never seen that in my life before. I know sin2+cos2=1.

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Updated: January 31, 2006
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