Subscribe to our YouTube channel for the latest videos, updates, and tips.
2 arccos(x) = arccos(2x2 - 1)
We will learn how to prove the property of the inverse trigonometric function 2 cos−1 x = cos−1 (2x2 - 1) or, 2 arccos(x) = arccos(2x2 - 1).
Proof:
Let, cos−1 x = α
Therefore, cos α = x
Now, cos 2α = 2 cos2 α - 1
cos 2α = 2x2 - 1
Therefore, 2α = cos−1 (2x2 - 1)
2 cos−1 x = cos−1 (2x2 - 1)
or, 2 arccos(x) = arccos(2x2 - 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) = π2
- arctan(x) + arccot(x) = π2
- arctan(x) + arctan(y) = arctan(x+y1−xy)
- arctan(x) - arctan(y) = arctan(x−y1+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
-
Worksheet on Average | Word Problem on Average | Questions on Average
May 19, 25 02:53 PM
In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems. -
8 Times Table | Multiplication Table of 8 | Read Eight Times Table
May 18, 25 04:33 PM
In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40 -
How to Find the Average in Math? | What Does Average Mean? |Definition
May 17, 25 04:04 PM
Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities. -
Problems Based on Average | Word Problems |Calculating Arithmetic Mean
May 17, 25 03:47 PM
Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed. -
Rounding Decimals | How to Round a Decimal? | Rounding off Decimal
May 16, 25 11:13 AM
Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate
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.