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Answer 1 · 2018-02-03T02:28:39

$[B]$ $color(green)( sqrt3 / 3$

let $x$ be the angle.

$x = cos ^(-1) ((sqrt3)/2)$

i.e. $cos x = sqrt3 / 2$

We know, $cos (30^@) = sqrt3 / 2$

$:. x = 30^@$

Replacing $cos^(-1) (sqrt3/2)$ with $x$ in the given sum,

$tan [cos^(-1) (sqrt3/2)] = tan x = tan 30^@ = 1/sqrt3$

Multiply $RHS$ by $sqrt3/sqrt3$ ,

$tan 30^@ = (1/sqrt3) * (sqrt3/sqrt3) = color(green)(sqrt3 / 3)$