Question

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

Answer 1

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

Explanation:

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`