Verify the hyperbolic identites

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Homework Statement



verify these identities:

1) tanh^2 x + sech^2 x =1
2) sinh(x+y) = sinh cosh y + cosh x sinh y


Homework Equations



cosh2x - sinh2x = 1
sech2x + tanh2x = 1
coth2x - csch2x = 1

sinh (x ± y) = sinh x cosh y ± cosh x sinh y
cosh (x ± y) = cosh x cosh y ± sinh x sinh y
tanh(x ± y) = (tanh x ± tanh y)/(1 ± tanh x.tanh y)
coth(x ± y) = (coth x coth y ± l)/(coth y ± coth x)
 
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Um, the identities are given to you in your "relevant equations." What is it you are asking?
 
Pretty sure you are suppose to show us what you did first..
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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