Simultaneous Trig Problem

[matthew042]

I am given this:
[attachment=0:qk57glhp]Equations.png[/attachment:qk57glhp]

With the conditions that ? is greater than or equal to 0 degrees and ? is less than or equal to 180 degrees.
Solve for cos(?+?)

I squared both equations, added them, and simplified with the cos^2 + sin^2 = 1 identity and got to:
sin?sin?+cos?cos? = 0

It is asking for cos(?+?) and not cos(?-?)
This is where I am stuck. Any help would be greatly appreciated.

 

[Deleted member 4993]

I am given this:
[attachment=0:2rvs5335]Equations.png[/attachment:2rvs5335]

With the conditions that ? is greater than or equal to 0 degrees and ? is less than or equal to 180 degrees.
Solve for cos(?+?)

I squared both equations, added them, and simplified with the cos^2 + sin^2 = 1 identity and got to:
sin?sin?+cos?cos? = 0

It is asking for cos(?+?) and not cos(?-?)
This is where I am stuck. Any help would be greatly appreciated.

\(\displaystyle \alpha \ - \ \beta \ = \ \frac{\pi}{2}\)

\(\displaystyle \alpha \ = \ \beta \ + \ \frac{\pi}{2}\)

\(\displaystyle cos(\alpha) \ = \ cos(\beta \ + \ \frac{\pi}{2}) \ = \ -sin(\beta)\)

Now continue....