Question

How do I prove this:
(cos x+cos y)^2=(sin x–sin y)^2 = 2+2cos(x + y)

Answer 1

after expanding left side
--> 2 + 2cos x*cos y - 2sin x*sin y
--> 2+2( cosx*cosy-sinx*siny)
recognize cosine angle sum formula: cos(a-b) = cosa*cosb-sina*sinb

--> 2+2cos(x+y)

Answer 2

I expand the LHS and got:
cos^2(x)+cos(x)cos(y)+cos(y)cos(x)+cos^2(y)
Is that correct?

Answer 3

yes, wait i assumed that was a plus sign in between , is it an equal sign ??

Answer 4

Has to be, for it to work....

Answer 5

right

Answer 6

It is an equal sign that is what my teacher gave us, I guess she wrote the problem wrong.