#tan( cos^-1(- sqrt3/2))# .Let #cos^-1(- sqrt3/2)=theta#
#:. cos theta = - sqrt3/2; cos 150 = - sqrt3/2 # and
#cos 210 = - sqrt3/2 :. theta = 150^0 and theta=210^0 #
#tan( cos^-1(- sqrt3/2)) =tan theta #. When #theta = 150^0 #
#tan theta= -1/sqrt3 and theta = 210^0 , tan theta= 1/sqrt3 #
#tan( cos^-1(- sqrt3/2)) = +- 1/sqrt3# [Ans]