Question 881003
The exact values of the trigonometric functions of {{{"0"}}} , {{{pi/6}}} , {{{pi/4}}} , {{{pi/3}}} , and {{{pi/2}}} are well known.
 
{{{cos(pi/6)=sqrt(3)/2}}}
{{{tan(pi/3)=sqrt(3)}}}
In this problem, {{{tan^(-1)(sqrt(3))}}} means the inverse tangent function, the angle whose tangent is {{{sqrt(3)}}} ,
which happens to be {{{pi/3}}},
but the cotangent of any angle is the reciprocal of the tangent (if they both exist), so we know that 
{{{cot(tan^(-1)(sqrt(3)))=1/sqrt(3)=sqrt(3)/3}}} ,
just as we also knew that {{{cot(pi/3)=sqrt(3)/3}}}
Putting it all together,
{{{cos(pi/6)+cot(tan^(-1)(sqrt(3)))=sqrt(3)/2+sqrt(3)/3=3sqrt(3)/6+2sqrt(3)/6=highlight(5sqrt(3)/6)}}}