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

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Answer 1 · 2018-04-01T16:22:09

Use the identity:

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

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

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

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

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

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