Trigonometry
posted by dan .
cos 17pi/6 + tan 17pi/6

Perhaps you might find it easier to think in degrees ?
17π/6 radians = 510°
which is coterminal with 150°
cos 150° =  cos30° = √3/2 , by CAST rule
tan 150 =  tan30 = 1/√3
so cos 17π/6 + tan 17π/6
= √3/2  1√3 , but 1/√3 = √3/3
= √3/2  √3/3
= ( 3√3  2√3)/6 = 5√3/6