Question

cos 17pi/6 + tan 17pi/6

Answer 1

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