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
● Inverse Trigonometric Functions
11 and 12 Grade Math
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