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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