Cos (pi + x) + cos (pi-x) ?

1 Answer
Mar 1, 2018

color (blue)(-2cos x)

Explanation:

We have
Cos (pi + x) + cos (pi-x)

Identities that we are going to use are as follows
color (red)(cos (a+b)=cos a cos b-sin a sin b)
And

color (red)(cos (a-b)=cos a cos b+sin a sin b)

It is quite clear that
cos (a-b)+cos (a+b)=2cos a cos b

Plugging in values for a and b, we get
Cos (pi + x) + cos (pi-x)=2cos pi cos x=-2cos x {Note:cos pi=-1}