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

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Answer 1 · 2016-06-21T12:20:47

#+-240/161#.

Let #a = arc sin (-8/17)#. Then #sin a = -8/17<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 = +-8/15#.

Now, the given expression is

#tan 2a = (2 tan a)/(1-tan^2a)#

#=+-(16/15)/(1-8^2/15^2)#

#=+-240/161#..