# 2 arcsin(x) = arcsin(2x$$\sqrt{1 - x^{2}}$$)

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

Proof:

Let, sin$$^{-1}$$ x = α

Therefore, sin α = x

Now, sin 2α = 2 sin α cos α

sin 2α = 2 sin α $$\sqrt{1 - sin^{2}α}$$

sin 2α = 2x . $$\sqrt{1 - x^{2}}$$

sin 2α =  2x$$\sqrt{1 - x^{2}}$$

Therefore, 2α = sin$$^{-1}$$ (2x$$\sqrt{1 - x^{2}}$$)

2 sin$$^{-1}$$ x = sin$$^{-1}$$ (2x$$\sqrt{1 - x^{2}}$$).

or, 2 arcsin(x) = arcsin(2x$$\sqrt{1 - x^{2}}$$)             Proved

Inverse Trigonometric Functions

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Fraction as a Part of Collection | Pictures of Fraction | Fractional

Feb 24, 24 04:33 PM

How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

2. ### Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Feb 24, 24 04:11 PM

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

3. ### Identification of the Parts of a Fraction | Fractional Numbers | Parts

Feb 24, 24 04:10 PM

We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

4. ### Numerator and Denominator of a Fraction | Numerator of the Fraction

Feb 24, 24 04:09 PM

What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.