How do you evaluate $sec(2 arcsin(-1/3))$ ?

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Answer 1 · 2016-07-19T03:25:21

$9/7$

Let $a = arc sin (-1/3)$ . Then,

$sin a = (-1/3)$ .

So, $cos 2 a=1-2 sin^2 a= 1 - 2 (1/9)=7/9$

The given expression is $sec 2 a=1/(cos 2a) =9/7$ ..

How do you evaluate sec(2 arcsin(-1/3)) sec(2 arcsin(-1/3))?