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

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Answer 1 · 2018-04-01T16:22:09

Use the identity:

$cos(2A) = 1-2sin^2(A)$

where $A = sin^-1(x)$

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

Substitute $sin^2(sin^-1(x)) = x^2$

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

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