Question

How do you do simplify `sin [2 tan^-1 (-2)]`?

Answer 1

`-4/sqrt5`.

Explanation:

Let `a = tan^(-1)(-2`.

`tan a = -2`.

As tan a is negative , sin a and cos a have opposite signs.
So, `sin a = +-2/sqrt5` and, correspondingly,`cos a = -1/sqrt5 or 1/sqrt5`.
The given expression is `sin 2a = 2 sin a cos a = -4/5`.