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

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Answer 1 · 2016-07-07T07:03:56

$cos(2sin^-1x)=1-2x^2.$

Let $sin^-1x=theta$ , so that, $x=sintheta, |x|<=1, theta in [-pi/2,pi/2].$

Now, Reqd. Value $= cos(2sin^-1x)=cos2theta=1-2sin^2theta=1-2x^2.$

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