Solve cosxcos(-x) - sinxsin(-x) = 1

[ravey_dotson]

cosxcos(-x) - sinxsin(-x) = 1

I know I'm making it harder than it is, but I can't seem to figure it out.
Any help would be appreciated.

RaveN

 

[Dick]

cos(-x)=cos(x). sin(-x)=-sin(x).

 

[ravey_dotson]

When I plugged those in then I get cosx2 - sinx2 = 1 and then I get completely lost.

 

[Dick]

When I plug them in I get cos(x)^2+sin(x)^2=1. There are two minus signs associated with the sin(x)^2.

 

[ravey_dotson]

Because it's -sin to begin with. I knew I was making it too hard. Thanks.

 

[Hurkyl]

Another way: isn't the l.h.s. in the form of an angle addition formula?

 

[HallsofIvy]

Not with the correct signs! It's cos²(x)+ sin²(x)!

 

[Dick]

It is cos(x+(-x)). That is another way to do it.