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
- General and Principal Values of sin\(^{-1}\) x
- General and Principal Values of cos\(^{-1}\) x
- General and Principal Values of tan\(^{-1}\) x
- General and Principal Values of csc\(^{-1}\) x
- General and Principal Values of sec\(^{-1}\) x
- General and Principal Values of cot\(^{-1}\) x
- Principal Values of Inverse Trigonometric Functions
- General Values of Inverse Trigonometric Functions
- arcsin(x) + arccos(x) = \(\frac{π}{2}\)
- arctan(x) + arccot(x) = \(\frac{π}{2}\)
- arctan(x) + arctan(y) = arctan(\(\frac{x + y}{1 - xy}\))
- arctan(x) - arctan(y) = arctan(\(\frac{x - y}{1 + xy}\))
- arctan(x) + arctan(y) + arctan(z)= arctan\(\frac{x + y + z – xyz}{1 – xy – yz – zx}\)
- arccot(x) + arccot(y) = arccot(\(\frac{xy - 1}{y + x}\))
- arccot(x) - arccot(y) = arccot(\(\frac{xy + 1}{y - x}\))
- arcsin(x) + arcsin(y) = arcsin(x \(\sqrt{1 - y^{2}}\) + y\(\sqrt{1 - x^{2}}\))
- arcsin (x) - arcsin(y) = arcsin (x \(\sqrt{1 - y^{2}}\) - y\(\sqrt{1 - x^{2}}\))
- arccos (x) + arccos(y) = arccos(xy - \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))
- arccos(x) - arccos(y) = arccos(xy + \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))
- 2 arcsin(x) = arcsin(2x\(\sqrt{1 - x^{2}}\))
- 2 arccos(x) = arccos(2x\(^{2}\) - 1)
- 2 arctan(x) = arctan(\(\frac{2x}{1 - x^{2}}\)) = arcsin(\(\frac{2x}{1 + x^{2}}\)) = arccos(\(\frac{1 - x^{2}}{1 + x^{2}}\))
- 3 arcsin(x) = arcsin(3x - 4x\(^{3}\))
- 3 arccos(x) = arccos(4x\(^{3}\) - 3x)
- 3 arctan(x) = arctan(\(\frac{3x - x^{3}}{1 - 3 x^{2}}\))
- Inverse Trigonometric Function Formula
- Principal Values of Inverse Trigonometric Functions
- Problems on Inverse Trigonometric Function
11 and 12 Grade Math
From 2 arccos(x) to HOME PAGE
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
-
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 11, 24 09:08 AM
2nd grade geometry worksheet -
Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical
Dec 09, 24 10:39 PM
What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver… -
Points and Line Segment | Two Points in a Curved Surface | Curve Line
Dec 09, 24 01:08 AM
We will discuss here about points and line segment. We know when two lines meet we get a point. When two points on a plane surface are joined, a straight line segment is obtained. -
Solid Shapes | Basic Geometric Shapes | Common Solid Figures | Plane
Dec 08, 24 11:19 PM
We will discuss about basic solid shapes. We see a variety of solid objects in our surroundings. Solid objects have one or more shapes like the following. Match the objects with similar shape. -
2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Dec 07, 24 03:38 PM
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.