Chapter 2: Q16P (page 71)

Verify each of the following by using equations (11.4), (12.2), and (12.3).
$tani z = i tanhz$

Short Answer

Expert verified

The equation $tani z = i tanhz$ is verified using the equations (11.4), (12.2) and (12.3).

Step by step solution

Given Information

Givenequationis $tani z = i tanhz$ .

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 equation is, $tani z = i tanhz$ .

Write $\tan z$ as $\tan (z) = \frac{\sin (z)}{\cos (z)}$

Let $z \to z i$ than $\tan (z i) = \frac{\sin (z i)}{\cos (z i)} \dots . (1)$ Use the following results.

$\cos (i z) = \cos h (z) \sin (i z) = i \sin h (z)$

Substitute the results in equation (1).

$\tan (i z) = \frac{i \sin h (z)}{\cos h (z)} \tan (i z) = i \tan h (z)$

Hence, the equation is verified.

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Verify each of the following by using equations (11.4), (12.2), and (12.3).
$tani z = i tanhz$

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).taniz=itanhz

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

Electromagnetism

Radiation

Physics of Motion

Solid State Physics

Astrophysics

Electrostatics

Study anywhere. Anytime. Across all devices.

Verify each of the following by using equations (11.4), (12.2), and (12.3).
$tani z = i tanhz$