Why do most of the book represent Plane waves by considering a single sine or cosine wave? There should be many, right? Isn't it misrepresentation? 
This Image is from Electrodynamics by Griffiths. Here also a monochromatic electromagnetic wave is considered.
 A: Note: This is answer is not specific to electromagnetic waves.
Short answer: yes, this an over simplification, but a useful one.
In general, the 1-dimensional wave equation (where $c$ is the speed of propagation)
$$\frac{\partial^2u}{\partial t^2} = c^2\frac{\partial^2u}{\partial x^2}$$
has solutions of the form
$$u(x,t) = F(x-ct) + G(x+ct)$$
where $F(x)$ and $G(x)$ are arbitrary functions.
The usefulness of representing a plane wave as a sinusoid results from being able to represent pretty much all such functions as a linear superposition of sinusoids as these represent the plane wave frequency eigenmodes.  This means we can write the wave equation solution as
$$u(x,t) = \int^\infty_{-\infty}s_+(\omega)e^{-i(kx+\omega t)}d\omega + \int^\infty_{-\infty}s_-(\omega)e^{-i(kx-\omega t)}d\omega$$
$$= \int^\infty_{-\infty}s_+(\omega)e^{-i(x+ct)}d\omega + \int^\infty_{-\infty}s_-(\omega)e^{-i(x-ct)}d\omega$$
where $F(x-ct) = \int^\infty_{-\infty}s_+(\omega)e^{-i(x+ct)}d\omega$ and $G(x+ct) = \int^\infty_{-\infty}s_-(\omega)e^{-i(x-ct)}d\omega$
$s_+(\omega)$ and $s_-(\omega)$ represent the frequency components of the forward and reverse propagating waves.
A lot more information is available in the Wikipedia article Wave equation.
A: A plane wave means a field where the field vector points in the same plane everywhere in the field. For instance, the field
$$ \vec{E}(z,t) = \sin(kz-\omega t)\vec{e_x}$$
is a field that oscillates in time, and oscillates along the z-axis, and always points along the (positive or negative) x-axis, as in your diagram. Only a single sine is necessary to model this.
A: The reason is mostly practicality & convenience

*

*Sines, cosines and complex exponentials are solutions to most wave equations

*For linear systems, you can break down any problem into solving for monochromatic first and than assembling the result using superposition

The hard way

*

*Solve wave equation for arbitrary input signal

The easier way

*

*Break down arbitrary signal into complex exponentials (or equivalent)

*Solve the wave equation for the complex exponentials

*Sum the results for the final solution.

