Prove that 2\arcsin(x)=\arccos(1-2x^2) for x\in(0,1)

Suman Cole

Suman Cole

Answered question


Prove that
2arcsin(x)=arccos(12x2) for x(0,1)

Answer & Explanation



Skilled2021-08-21Added 107 answers

We have two ways to demonstrate this. The first is by employing function derivatives. Secondly, by applying trigonometric 

Let F(x)=2arcsin(x), and G(x)=arccos(12x2)
 F(x)=G(x), so
21x2, therefore F(x)=G(x)
In order to confirm that a constant is '0,' this means that F(x) and G(x) must differ by a constant. Replace with any value of the x test that you like, such as 0. F(0)=2arcsin(0)=0 while G(0)=arccos(2)=0 constant is zero. So, F(x)=G(x)2arcsin(x)=arccos(12x2)

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