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

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

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

$=+-240/161$ ..

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