5859 Prove the identities. (a) 1 tanh2 x = sech2 x(b) tanh(x + y) = tanh x + tanh y1 +

Chapter 6, Problem 59

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58-59 Prove the identities.

(a) $1-\tanh ^{2} x=\operatorname{sech}^{2} x$

(b) $\tanh (x+y)=\frac{\tanh x+\tanh y}{1+\tanh x \tanh y}$

Equation Transcription:

$1-{tanh}^{2}\ x={sech}^{2}\ x$

$tanh(x+y)=\frac{tanh\ x+tanh\ y}{1+tanh\ x\ tanh\ y}$

$tanh\ 2x=\frac{2\ tanh\ x}{1+{tanh}^{2}\ x}$

Text Transcription:

1-tanh^2 x=sech^2 x

tanh(x+y)=frac tanh x+tanh y / 1+tanh x tanh y

tanh 2x=frac 2 tanh x / 1+tanh^2 x

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