How do you simplify $cos(sin^-1(2/x))$ ?

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Answer 1 · 2016-04-29T12:46:37

$|x|>=2 and cos(sin^(-1)(2/x))=+-sqrt(x^2-4)/x$

Let $a=sin^(-1)(2/x)$ . Then $sin a=(2/x) and cos a=+-sqrt(x^2-4)/x$ .
So, $cos(sin^(-1)(2/x))=cos a=+-sqrt(x^2-4)/x$ .

How do you simplify cos(sin^-1(2/x)) cos(sin^-1(2/x))?