Question #ea6cb

1 Answer
sankarankalyanam · Surya K.
Feb 3, 2018

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

Explanation:

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)#

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