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Welcome to NRICH.

tanh(2x)

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By Philip Hassall (P885) on Thursday, October 12, 2000 - 02:41 pm:

I am trying to show that
tanh 2x = (2tanh x)/(1 + tanh²x)

Can anyone help!

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By James Cruise (P2088) on Thursday, October 12, 2000 - 03:05 pm:

Do you already know what sinh2x and cosh2x?

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By Thomas Mooney (P3048) on Thursday, October 12, 2000 - 04:31 pm:

Tanh2x=Tanh(x+x)=sinh(x+x)/cosh(x+x)

=(sinhxcoshx+sinhxcoshx)/(coshxcoshx+sinhxsinhx)
=2sinhxcoshx/cosh²(x)+sinh²(x)
Then divide by cosh²(x) to get the result.

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