# Question #7bdf4

##### 1 Answer

#### Explanation:

Use the trigonometric formula for the cosine of a sum of angles:

Now expand

That is:

To obtain a more compact expression, we can use the properties of trigonometric functions.

Write the series as:

and analyze the coefficients

#c_0 = cosa#

#c_1 = -sina = cos(a+pi/2)#

#c_2 = -cosa = cos(a+pi)#

#c_3 = sina = cos(a+(3pi)/2)#

#...#

and we can see that the series can be written as: