Please add comments line for matlab and show all step in paper, ASAP. Thanks in advance....

Question (a)

We know that

Let

So

So

Question (b)

We know that

Let

So

So

Question (c)

This means that will be always greater than 1.

Question (d)

We know

So

Hence proved.

Question (e)

MATLAB Code

clc;
clear all;
close all;

th = -10:0.00001:10; % The range of theta for which the function is to be plotted
y1 = (exp(th) + exp(-th))/2; % Evaluating hyperpolic cosine
y2 = (exp(th) - exp(-th))/2; % Evaluating hyperpolic sine

plot(th,y1,'linewidth',2); % Plotting hyperpolic cosine
grid
xlabel('\theta');
ylabel('cosh(\theta)');
title('The hyperbolic cosine function');

figure
plot(th,y2,'linewidth',2); % Plotting hyperpolic sine
grid
xlabel('\theta');
ylabel('sinh(\theta)');
title('The hyperbolic sine function');

After executing, we get

ejx +e-jx cos(x) = ?

x= je

=(!)so! !!-a + arxra

= ()s05 + - 0.

cos(je) = cosh(O)

e-e tee cosh(O) = 2

لازم - لازم sin(x) =

x= je

ejxje-e-jxje sin(jo) = j2

e-o-e sin(je) = = 12

j sin(je) =

-1 sin(jo) – (- -j sin(je) =

-j sin(je) = sinh(0)

sinh(0) = eº - e-º

e-e tee cosh(O) = 2

+ cosh(O) = 2

cocco 1+ 2e cosh(0) = 2e

1 cosh(O) = 300+1

cosh(O)

sinh(0) = eº - e-º

sinh(-) = 2

sinh(-) = -sinh(0)

sinh(0) = - sinh(-)

The hyperbolic cosine function 12000 10000 8000 cosho) 4000 2000 H -10 0

104 The hyperbolic sine function 15 sinh(0)