`cos(120 + 45), cos(120) + cos(45)` Find the exact value of the expression.

Given `cos(120+45)`

`cos(u+v)=cos(u)cos(v)-sin(u)sin(v)`

`cos(120+45)=cos(120)cos(45)-sin(120)sin(45)`

`cos(120+45)=(-1/2)(sqrt2/2)-(sqrt3/2)(sqrt2/2)=-sqrt2/4-sqrt6/4=(-sqrt2-sqrt6)/4`

Given `cos(120)+cos(45)`

`cos(120)+cos(45)=(-1/2)+sqrt2/2=(-1+sqrt2)/2`

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Given `cos(120+45)`

`cos(u+v)=cos(u)cos(v)-sin(u)sin(v)`

`cos(120+45)=cos(120)cos(45)-sin(120)sin(45)`

`cos(120+45)=(-1/2)(sqrt2/2)-(sqrt3/2)(sqrt2/2)=-sqrt2/4-sqrt6/4=(-sqrt2-sqrt6)/4`

Given `cos(120)+cos(45)`

`cos(120)+cos(45)=(-1/2)+sqrt2/2=(-1+sqrt2)/2`

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