How do you simplify $tan[cos^-1(-sqrt(3)/2)]$ ?

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Answer 1 · 2016-04-15T09:38:31

$tan[cos^(-1)(-sqrt3/2)]=+-1/sqrt3$

As $cos(pi/6)=sqrt3/2$ we have $cos(pi-pi/6)=-sqrt3/2$

$cos^(-1)(-sqrt3/2)=+-(pi-pi/6)=+-((5pi)/6)$

Hence $tan[cos^(-1)(-sqrt3/2)]=tan+-(pi-pi/6)=+-1/sqrt3$

How do you simplify tan[cos^-1(-sqrt(3)/2)]tan[cos^-1(-sqrt(3)/2)]?