Chapter 2: Q7P (page 71)

Verify each of the following by using equations (11.4), (12.2), and (12.3).
sinh 2z=2 sinh z cosh z

Short Answer

Expert verified

The equation sinh 2z=2 sinh z cosh z is verified using the equations (11.4), (12.2) and (12.3).

Step by step solution

Given information

The given equation is sinh 2z=2 sinh z cosh z.

Definition of Hyperbolic Function.

A relationship between the distances from a point on a hyperbola to the origin and the coordinate axes, represented as a function of an angle is called Hyperbolic Function.

Use exponential form to expand the equation

The exponential form of the given equation is,

$\sin h 2 z = \frac{e^{2 z} - e^{- 2 z}}{2}$ …. (1)

Use identity $x^{2} - y^{2} = (x + y) (x - y)$ to split the numerator of equation (1).

$\sinh 2 \frac{(e^{z} + e^{- z}) (e^{z} - e^{- z})}{2}$ …(2)

Multiply the equation (2) by $\frac{2}{2}$ .

$\sin h 2 z = \frac{(e^{z} + e^{- z}) (e^{z} - e^{- z})}{2} \times \frac{2}{2} \sin h 2 z = 2 \times \frac{(e^{z} + e^{- z})}{2} \times \frac{(e^{z} - e^{- z})}{2}$

Put $\frac{(e^{z} - e^{- z})}{2} = \cos h z$ .

Put $\frac{(e^{z} - e^{- z})}{2} = s inh z$ .

sinh z=2 cosh z. sinh 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).
sinh 2z=2 sinh z cosh z

Short Answer

Step by step solution

Given information

Definition of Hyperbolic Function.

Use exponential form to expand the equation

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Verify each of the following by using equations (11.4), (12.2), and (12.3).sinh 2z=2 sinh z cosh z

Short Answer

Step by step solution

Given information

Definition of Hyperbolic Function.

Use exponential form to expand the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Translational Dynamics

Circular Motion and Gravitation

Radiation

Electric Charge Field and Potential

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.

Verify each of the following by using equations (11.4), (12.2), and (12.3).
sinh 2z=2 sinh z cosh z