Q24MP - Mathematical Methods in Physical Sciences

Question

Verify the formulas in Problems 17 to 24.

$\mathbf{cosh}\mathbf{ }\mathbf{iz}\mathbf{=}\mathbf{cosz}$

Step-by-Step Solution

Answer

The formula $\cosh \mathrm{iz}=\mathrm{cosz}$ is verified

Step 1: Given Information

Given formula is $\cosh \mathrm{iz}=\mathrm{cosz}$.

Step 2: Definition of Trigonometric equation.

A trigonometric equation is one that has one or more trigonometric ratios with unknown angles.

Step 3: Use exponential form to expand the equation

Given the function $\cosh \mathrm{iz}=\mathrm{cosz}$.

 

Write the exponential form of the cosh(z) .

$$\begin{gathered} \cos h\left(z\right)=\frac{e^{\left(z\right)}+e^{\left(-z\right)}}{2} \\ \cos h\left(iz\right)=\frac{e^{\left(iz\right)}+e^{\left(-iz\right)}}{2} \\ =\cos \left(z\right) \end{gathered}$$

 

Hence the formula is verified.