Question

If E1 = Eo Cos(w t) and E2 = Eo Cos(w t + theta):

a) Derive an expression for E = E1 + E2.

A) E = 2Eo Cos(theta/2) Cos(w t + theta/2)
B) E = Eo Sin(w t + theta)
C) E = Eo Cos(theta) Sin(w t)
D) E = Eo Cos(theta/2) Sin(w t + theta/2)

Answer 1

To derive the expression for E = E1 + E2, we can add the two given expressions and apply a trigonometric identity.

Step-by-step explanation:

To derive an expression for E = E1 + E2, we need to add the two given expressions:

E = E1 + E2 = Eo Cos(w t) + Eo Cos(w t + theta).

Using the trigonometric identity cos(u) + cos(v) = 2 cos((u+v)/2) cos((u-v)/2), we can rewrite the equation as:

E = 2Eo cos(theta/2) cos(w t + theta/2).

So, the correct answer is option A) E = 2Eo Cos(theta/2) Cos(w t + theta/2).