How do you calculate tan(2arcsin(-8/17))tan(2arcsin(817))?

1 Answer
Jun 21, 2016

+-240/161±240161.

Explanation:

Let a = arc sin (-8/17)a=arcsin(817). Then sin a = -8/17<0.sina=817<0..

So, a is in either 3rd quadrant or in the 4th. Accordingly,

cos a = +-sqrt(1-8^2/17^2)=+- 15/17 and tan a = +-8/15cosa=±182172=±1517andtana=±815.

Now, the given expression is

tan 2a = (2 tan a)/(1-tan^2a)tan2a=2tana1tan2a

=+-(16/15)/(1-8^2/15^2)=±1615182152

=+-240/161=±240161..