# 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

Inverse Trigonometric Functions