How do you simplify $sin (tan^-1 (-3))$ ?

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Answer 1 · 2016-07-08T08:04:15

$-3/sqrt 10$ , for principal value of $tan^(-1)(-3)$ . The general solution is $+-3/sqrt 10$ .

Let $a=tan^(-1)(-3)$ . Then, $tan a = -3<0$ .

So, the principal a is in the fourth quadrant and the general a is in

either fourth or second.

And so, $sin a = -3/sqrt 10$ against principal a and the given

expression

$sin a=-3/sqrt 10$

The general solution is $+-3/sqrt 10$ .

How do you simplify sin (tan^-1 (-3))sin (tan^-1 (-3))?