Question

How do you evaluate `Tan (sin^-1 (2/3))`?

Answer 1

Conventional value is `2/sqrt5` and the general value is `+-2/sqrt5`.

Explanation:

Let `a=sin^(-1)(2/3) in Q_1` for the conventional principal value and

also `in Q_2`, for the general value.

The given expression is tan a

`=sin a/cos a=(2/3)/(+-sqrt(1-(2/3)^2))=+-2/sqrt5`.

Conventional value is `2/sqrt5` and the general value is `+-2/sqrt5`.