The angle sum identity for cosine is:
[tex]cos( \theta+ \beta) = cos( \theta)cos( \beta) - sin( \theta)sin( \beta)[/tex]
So we need to figure out the values of \theta and \beta.
[tex]tan^{-1}( \frac{1}{2}) = \theta [/tex]
[tex]cos^{-1}( \frac{2}{3} ) = \beta[/tex]
[tex]cos(tan^{-1}( \frac{1}{2}))cos(cos^{-1}(\frac{2}{3})) - sin(tan^{-1}( \frac{1}{2}))sin(cos^{-1}(\frac{2}{3})) = [/tex] 0.26295 rad
