(C) Substituting the definition of $\tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$,we get:$\frac{1+\tanh x}{1-\tanh x} = \frac{1 + \frac{e^x - e^{-x}}{e

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(C) Substituting the definition of $\tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$,we get:$\frac{1+\tanh x}{1-\tanh x} = \frac{1 + \frac{e^x - e^{-x}}{e^x + e^{-x}}}{1 - \frac{e^x - e^{-x}}{e^x + e^{-x}}}$$= \frac{\frac{e^x + e^{-x} + e^x - e^{-x}}{e^x + e^{-x}}}{\frac{e^x + e^{-x} - (e^x - e^{-x})}{e^x + e^{-x}}}$$= \frac{2e^x}{2e^{-x}}$$= e^{x - (-x)} = e^{2x}$

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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The value of $\frac{1+\tanh x}{1-\tanh x}$ is

AP EAMCET 2022 All AP EAMCET

A
$e^x$
B
$e^{-2x}$
C
$e^{2x}$
D
$e^{-x}$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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