2 arccos(x) = arccos(2x\(^{2}\) - 1)

We will learn how to prove the property of the inverse trigonometric function 2 cos\(^{-1}\) x = cos\(^{-1}\) (2x\(^{2}\) - 1) or, 2 arccos(x) = arccos(2x\(^{2}\) - 1).

Proof:

Let, cos\(^{-1}\) x = α                 

Therefore, cos α = x

Now, cos 2α = 2 cos\(^{2}\) α - 1

cos 2α = 2x\(^{2}\) - 1

Therefore, 2α = cos\(^{-1}\) (2x\(^{2}\) - 1)

2 cos\(^{-1}\) x = cos\(^{-1}\) (2x\(^{2}\) - 1)    

or, 2 arccos(x) = arccos(2x\(^{2}\) - 1).                 Proved















11 and 12 Grade Math

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