What is the exact value of the expression?
tan (pi/6) = tan (30°) = √3/3
sin (5pi/3 )= sin (-60°)= -√3/2
cos (-3pi/4) = cos ( 360 - 135 ) = cos (225°) = -√2/2
So
√3/3 + ( -√3/2) (-√2/2) =
√3/3 + √6/4 = (common den = 12 )
4√3 + 3√6
__________
12