Chapter 2: Q17P (page 71)

Verify each of the following by using equations (11.4), (12.2), and (12.3).
$t a n h i z = i t a n z$

Short Answer

Expert verified

The equation $\tan h i z = i \tan z$ is verified using the equations (11.4), (12.2) and (12.3).

Step by step solution

Given Information

Given equation is $\tan h i z = i \tan z$

Definition of Hyperbolic Function.

A hyperbolic function is a representation of the relationship between a point's distances from the origin to the coordinate axes as a function of an angle.

Simplify and Prove the Right Hand Side(RHS) of given equation.

Given the equationis, $tanhi z = i tanz$ .

Write role="math" localid="1658898114792" $\tan h z$ as $\tan h (z) = \frac{\sin h (z)}{\cos h (z)}$

Let $z \to z i$ than role="math" localid="1658898255354" $\tanh (zi) = \frac{\sinh (zi)}{\cosh (zi)}$ ….(1)

Solve Left hand side(LHS) i.e,.

role="math" localid="1658898371496" $\tanh (zi) = \frac{\sinh (zi)}{\cosh (zi)} = (\frac{e^{(z i)} - e^{(- z i)}}{2}) (\frac{2}{e^{(z i)} + e^{(- z i)}})$

Multiply numerator and denominator by

$\tanh (zi) = (\frac{e^{(zi)} - e^{(- zi)}}{2}) (\frac{2}{e^{(zi)} + e^{(- zi)}}) \times \frac{i}{i} \tanh (zi) = (\frac{e^{(zi)} - e^{(- zi)}}{2 i}) (\frac{2}{e^{(zi)} + e^{(- zi)}}) \tanh (zi) = i \sin (z) \cos (z)$

Hence, the equation is verified.

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Verify each of the following by using equations (11.4), (12.2), and (12.3).
$t a n h i z = i t a n z$

Short Answer

Step by step solution

Given Information

Definition of Hyperbolic Function.

Simplify and Prove the Right Hand Side(RHS) of given equation.

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Verify each of the following by using equations (11.4), (12.2), and (12.3).tanhiz=itanz

Short Answer

Step by step solution

Given Information

Definition of Hyperbolic Function.

Simplify and Prove the Right Hand Side(RHS) of given equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

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Study anywhere. Anytime. Across all devices.

Verify each of the following by using equations (11.4), (12.2), and (12.3).
$t a n h i z = i t a n z$