Question

How do you solve `csc[tan^-1 (-2)]`?

Answer 1

`csc(tan^(-1)(-2))=-sqrt5/2`

Explanation:

From the definition of inverse ratios, if `tan^(-1)(-2)=theta`, then `tantheta=-2`

As `tantheta=-2`, we have `cottheta=-1/2` and

`csctheta=-sqrt(1+(-1/2)^2)=-sqrt(1+1/4)`

= `-sqrt(5/4)=-sqrt5/2`

Note that as `tantheta` is negative so would be `csctheta` as domain for `theta` is `[-pi/2,pi/2]`.

hence `csctheta=csc(tan^(-1)(-2))=-sqrt5/2`