# Math Blog

### Problem on Change the Subject of a Formula | Changing the Subject

We will solve different types of problems on change the subject of a formula. The subject of a formula is a variable whose relation with other variables of the context is sought and the formula is written in such a way that subject is expressed in terms of the other

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### Worksheet on Change of Subject | Change the Subject as Indicated

Practice the questions given in the worksheet on change of subject When a formula involving certain variables is known, we can change the subject of the formula. What is the subject in each of the following questions? Change the subject as indicated.

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### Worksheet on Framing a Formula | Framing Formulas | Frame an Equation

Practice the questions given in the worksheet on framing a formula. I. Frame a formula for each of the following statements: 1. The side ‛s’ of a square is equal to the square root of its area A.

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### Establishing an Equation | Framing a Formula | Framing Linear Equation

We will discuss here about establishing an equation. In a given context, the relation between variables expressed by equality (or inequality) is called a formula. When a formula is expressed by an equality, the algebraic expression is called an equation.

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### Rectangular Cartesian Co-ordinates | Abscissa | Ordinate | Oblique Co-ordinate

What is Rectangular Cartesian Co-ordinates? Let O be a fixed point on the plane of this page; draw mutually perpendicular straight line XOX’ and YOY’ through O. Clearly, these lines divide the plane

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### What is Co-ordinate Geometry? | Analytical Geometry| Cartesian Co-ordinate

What is co-ordinate geometry? The subject co-ordinate geometry is that particular branch of mathematics in which geometry is studied with the help of algebra. This branch of mathematics was fir

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### Table of Tangents and Cotangents | Natural Tangents and Natural Cotangents

We will discuss here the method of using the table of tangents and cotangents. This table shown below is also known as the table of natural tangents and natural cotangents. Using the table we can

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### Table of Sines and Cosines |Trigonometric Table|Table of Natural sines & cosines

We will discuss here the method of using the table of sines and cosines: The above table is also known as the table of natural sines and natural cosines. Using the table we can find the values

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### Problems on Properties of Triangle | Angle Properties of Triangles

We will solve different types of problems on properties of triangle. 1. If in any triangle the angles be to one another as 1 : 2 : 3, prove that the corresponding sides are 1 : √3 : 2.

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### Properties of Triangle Formulae | Triangle Formulae | Properties of Triangle

We will discuss the list of properties of triangle formulae which will help us to solve different types of problems on triangle.

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### Law of Tangents |The Tangent Rule|Proof of the Law of Tangents|Alternative Proof

We will discuss here about the law of tangents or the tangent rule which is required for solving the problems on triangle. In any triangle ABC,

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### Area of a Triangle | ∆ = ½ bc sin A | ∆ = ½ ca sin B | ∆ = ½ ab sin C

If ∆ be the area of a triangle ABC, Proved that, ∆ = ½ bc sin A = ½ ca sin B = ½ ab sin C That is, (i) ∆ = ½ bc sin A (ii) ∆ = ½ ca sin B (iii) ∆ = ½ ab sin C

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### The Law of Cosines | The Cosine Rule | Cosine Rule Formula | Cosine Law Proof

We will discuss here about the law of cosines or the cosine rule which is required for solving the problems on triangle. In any triangle ABC, Prove that, (i) b$$^{2}$$

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### Proof of Projection Formulae | Projection Formulae | Geometrical Interpretation

The geometrical interpretation of the proof of projection formulae is the length of any side of a triangle is equal to the algebraic sum of the projections of other sides upon it. In Any Triangle

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### Projection Formulae | a = b cos C + c cos B | b = c cos A + a cos C

Projection formulae is the length of any side of a triangle is equal to the sum of the projections of other two sides on it. In Any Triangle ABC, (i) a = b cos C + c cos B

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### Theorem on Properties of Triangle | p/sin P = q/sin Q = r/sin R = 2K

Proof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circum-centre and R the circum-radius of any triangle PQR. Let O be the circum-centre and R

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### The Law of Sines | The Sine Rule | The Sine Rule Formula | Law of sines Proof

We will discuss here about the law of sines or the sine rule which is required for solving the problems on triangle. In any triangle the sides of a triangle are proportional to the sines

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###### Jan 20, 2018

In trigonometry we will discuss about the different properties of triangles. We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.

### Problems on Inverse Trigonometric Function | Inverse Circular Function Problems

We will solve different types of problems on inverse trigonometric function. 1. Find the values of sin (cos$$^{-1}$$ 3/5)

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### Principal Values of Inverse Trigonometric Functions |Different types of Problems

We will learn how to find the principal values of inverse trigonometric functions in different types of problems. The principal value of sin$$^{-1}$$ x for x > 0, is the length of the arc of a unit

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### Inverse Trigonometric Function Formula | Inverse Circular Function Formula

We will discuss the list of inverse trigonometric function formula which will help us to solve different types of inverse circular or inverse trigonometric function.

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### 3 arctan(x) | 3 tan$$^{-1}$$ x |3 tan inverse x | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function 3 arctan(x) = arctan($$\frac{3x - x^{3}}{1 - 3 x^{2}}$$) or, 3 tan$$^{-1}$$ x = tan$$^{-1}$$

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### 3 arccos(x) | 3 cos$$^{-1}$$ x |3 cos inverse x | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function 3 arccos(x) = arccos(4x$$^{3}$$ - 3x) or, 3 cos$$^{-1}$$ x = cos$$^{-1}$$ (4x$$^{3}$$ - 3x)

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### 3 arcsin(x) | 3 sin$$^{-1}$$ x |3 sin inverse x | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x - 4x$$^{3}$$) or, 3 sin$$^{-1}$$ x = sin$$^{-1}$$ (3x - 4x$$^{3}$$)

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### 2 arctan(x) | 2 tan$$^{-1}$$ x | 2 tan inverse x |Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function, 2 arctan(x) = arctan($$\frac{2x}{1 - x^{2}}$$) = arcsin($$\frac{2x}{1 + x^{2}}$$)

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### 2 arccos(x) | 2 cos$$^{-1}$$ x | 2 cos inverse x |Inverse Trigonometric Function

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).

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### 2 arcsin(x) | 2 sin$$^{-1}$$ x | 2 sin inverse x |Inverse Trigonometric Function

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$$\sqrt{1 - x^{2}}$$)

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### arccos(x) - arccos(y) | cos^-1 x - cos^-1 y | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function arccos(x) - arccos(y) = arccos(xy + $$\sqrt{1 - x^{2}}$$$$\sqrt{1 - y^{2}}$$)

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### arccos(x) + arccos(y) | cos^-1 x + cos^-1 y | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function arccos (x) + arccos(y) = arccos(xy - $$\sqrt{1 - x^{2}}$$$$\sqrt{1 - y^{2}}$$)

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### arcsin x - arcsin y |sin$$^{-1}$$ x - sin$$^{-1}$$ y|sin inverse x-sin inverse y

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

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### arcsin(x) + arcsin(y) |sin$$^{-1}$$ x+sin$$^{-1}$$ y|sin inverse x+sin inverse y

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

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### arccot(x) - arccot(y) | cot^-1 x - cot^-1 y | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function arccot(x) - arccot(y) = arccot($$\frac{xy + 1}{y - x}$$) (i.e., cot$$^{-1}$$ x + cot$$^{-1}$$ y = cot$$^{-1}$$

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### arccot(x) + arccot(y) | cot^-1 x + cot^-1 y | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function arccot(x) + arccot(y) = arccot($$\frac{xy - 1}{y + x}$$) (i.e., cot$$^{-1}$$ x - cot$$^{-1}$$ y = cot$$^{-1}$$

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### arctan(x) + arctan(y) + arctan(z) | tan^-1 x + tan^-1 y + tan^-1 z |Inverse Trig

We will learn how to prove the property of the inverse trigonometric function arctan(x) + arctan(y) + arctan(z) = arctan$$\frac{x + y + z – xyz}{1 – xy – yz – zx}$$ (i.e., tan$$^{-1}$$ x

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### arctan x + arccot x = π/2 | arctan(x) + arccot(x) = $$\frac{π}{2}$$ | Examples

We will learn how to prove the property of the inverse trigonometric function arctan(x) + arccot(x) = $$\frac{π}{2}$$ (i.e., tan$$^{-1}$$ x + cot$$^{-1}$$ x = $$\frac{π}{2}$$).

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### arctan x - arctan y | tan^-1 x - tan^-1 y | Inverse Trigonometric Function

We will learn how to prove the property of the inverse trigonometric function arctan(x) - arctan(y) = arctan($$\frac{x - y}{1 + xy}$$) (i.e., tan$$^{-1}$$ x - tan$$^{-1}$$ y

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### arctan(x) + arctan(y) = arctan($$\frac{x + y}{1 - xy}$$) | tan^-1 x + tan^-1 y

We will learn how to prove the property of the inverse trigonometric function arctan(x) + arctan(y) = arctan($$\frac{x + y}{1 - xy}$$), (i.e., tan$$^{-1}$$ x + tan$$^{-1}$$ y = tan$$^{-1}$$

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### Method of Substitution | The Substitution Method Examples

Steps involved in solving linear equations in two variables by method of substitution: Examine the question carefully and make sure that two different line

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### arcsin x + arccos x = π/2 | arcsin(x) + arccos(x) = $$\frac{π}{2}$$ | Examples

We will learn how to prove the property of the inverse trigonometric function arcsin(x) + arccos(x) = $$\frac{π}{2}$$. Proof: Let, sin$$^{-1}$$ x = θ Therefore, x = sin θ

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### General Values of Inverse Trigonometric Functions | Inverse Circular Functions

We will learn how to find the general values of inverse trigonometric functions in different types of problems. 1. Find the general values of sin$$^{-1}$$ (- √3/2)

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### General and Principal Values of cot$$^{-1}$$ x | Inverse Circular Functions

How to find the general and principal values of cot$$^{-1}$$ x? Let cot θ = x (- ∞ < x < ∞) then θ = cot$$^{-1}$$ x. Here θ has infinitely many values.

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### General and Principal Values of sec$$^{-1}$$ x | General values of arc sec x

How to find the general and principal values of sec$$^{-1}$$ x? Let sec θ = x ( I x I ≥ 1 i.e., x ≥ 1 or, x ≤ - 1 ) then θ = sec - 1x . Here θ has infinitely many values.

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### General and Principal Values of csc$$^{-1}$$ x | Inverse Circular Functions

How to find the general and principal values of ccs$$^{-1}$$ x? Let csc θ = x ( I x I ≥ 1 i.e., x ≥ 1 or, x ≤ - 1 ) then θ = csc - 1x . Here θ has infinitely many values.

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### General and Principal Values of tan$$^{-1}$$ x | Inverse Circular Functions

How to find the general and principal values of tan$$^{-1}$$ x? Let tan θ = x (- ∞ < x < ∞) then θ = tan$$^{-1}$$ x. Here θ has infinitely many values.

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### General and Principal Values of cos$$^{-1}$$ x | Inverse Circular Functions

How to find the general and principal values of cos$$^{-1}$$ x? Let cos θ = x where, (- 1 ≤ x ≤ 1) then θ = cos$$^{-1}$$ x. Here θ has infinitely many values.

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### Method of Elimination | Systems of Equations with Elimination

Earlier we have seen about linear equation in two variables and an overview of solution of linear equation in two variables. From this topic on wards, we

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### Solution of a Linear Equation in Two Variables |Method of Substitution, Elimi...

Earlier we have studied about the linear equations in one variable. We know that in linear equations in one variable, only one variable is present whose value we need to find out by doing calculations

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### Comparison between Simple Interest and Compound Interest | Solved Examples

Comparison between Simple Interest and Compound Interest for the same principal amount. Interest is of two kinds – Simple Interest and Compound Interest.

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### Worksheet on Compound Interest as Repeated Simple Interest | Answers

Practice the questions given in the Worksheet on Compound Interest as Repeated Simple Interest. 1. Find the amount and compound interest for \$2000 lent for 2 years at 2% rate of interest p.a.

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