Question

In triangle ABC given: `cos(A)=sqrt(2)//2` and `cos(B)=sqrt(3)//2`. Then, `cos(C)=`?

Answer 1

`cos(C)=(sqrt2-sqrt6)/4`

Explanation:

For `cos(A)=sqrt2/2`, `A=45` degrees and for `cos(B)=sqrt3/2`, `B=30` degrees. Hence `C=180-(45+30)=105` degrees.

Thus,

`cos105=-cos75=-(cos45*cos30-sin45*sin30)=(sqrt2-sqrt6)/4`