How do i verify these trig equations?

Question

cos(x+y)+cos(x-y) = 2(cosx)(cosy)

Answer 1

This equation is normally derived from the equations:
cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
By adding these together, you have the result immediately.

You could verify, but not prove them, by substituting several pairs of values for x and y, and checking that the LHS and the RHS gave the same results.

Answer 2

You have to use Trig identities, Search the web for trig identities and copy them into a file so you can print it out and use it as a reference when you are working problems like this.

Answer 3

Are you allowed to use cos(x+y) = cosx.cosy - sinx.siny
If so then cos(x-y) = cosx.cos-y - sinx.sin-y
and cos(-y) = cos(y) but sin-y = -sin(y)
so you get cosx.cosy -sinx.siny + cosx.cosy + sinx.siny
=2cosx.cosy

Answer 4

cos (x + y) = cos x.cosy - sinx.siny
cos (x - y) = cos x.cos y + sin x.sin y

cos (x + y) + cos (x - y) = 2.cos x.cos y

Answer 5

plugging them with values will check them once
and adding those from above will prove'em at glance