Need Help Solving cos -105 with sum or difference identity

Question

The question is cos -105. I know how to do the process for it but for some reason my answer doesn't have the right negatives.

I am getting:

 

√2 + (-√6)

--------------

        4

 

The actual answer is:

 

√2 - √6

-----------

      4

 

 

 

My process is:

cos 120 - 225 = -105

   1      √2           √3         √2

- __ * ____   +   ____ * - ____   =

 

   2        2             2            2

 

 

√2              √6

___   +   -  ____    =

 

  4                4

 

 

√2 + (-√6)

_________

       4

 

 

I don't know what I'm doing wrong. (Math is my weak point, and I struggle with negatives even more so, so I at least know that)

 

Please help! Thanks!

-A HS Junior in Trigonometry

P.S. the worksheet is from Kuta Software, so my teacher didn't create it.

 

Answer 1

If you have  (√2 + (-√6))/4=√2 -√6)/4. So your answer is correct!

(in multiplication +- gives -; that is 1*(-1)=-1)