Newly added pages can be seen from this page. Keep visiting to this page so that you will remain updated.

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

Continue reading "Area of a Triangle | ∆ = ½ bc sin A | ∆ = ½ ca sin B | ∆ = ½ ab sin C"

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

Continue reading "Proof of Projection Formulae | Projection Formulae | Geometrical Interpretation "

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

Continue reading "Projection Formulae | a = b cos C + c cos B | b = c cos A + a cos C"

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

Continue reading "The Law of Sines | The Sine Rule | The Sine Rule Formula | Law of sines Proof"

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.

Continue reading "Properties of Triangles | Semi-perimeter| Circum-circle|Circum-radius|In-radius "

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

Continue reading "Problems on Inverse Trigonometric Function | Inverse Circular Function Problems"

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)

Continue reading "General Values of Inverse Trigonometric Functions | Inverse Circular Functions "

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

Continue reading "Principal Values of Inverse Trigonometric Functions |Different types of Problems"

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.

Continue reading "Inverse Trigonometric Function Formula | Inverse Circular Function Formula"

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\(^{-1}\)

Continue reading "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 arccos(x) = arccos(4x\(^{3}\) - 3x) or, 3 cos\(^{-1}\) x = cos\(^{-1}\) (4x\(^{3}\) - 3x)

Continue reading "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 arcsin(x) = arcsin(3x - 4x\(^{3}\)) or, 3 sin\(^{-1}\) x = sin\(^{-1}\) (3x - 4x\(^{3}\))

Continue reading "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, 2 arctan(x) = arctan(\(\frac{2x}{1 - x^{2}}\)) = arcsin(\(\frac{2x}{1 + x^{2}}\))

Continue reading "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 cos\(^{-1}\) x = cos\(^{-1}\) (2x\(^{2}\) - 1) or, 2 arccos(x) = arccos(2x\(^{2}\) - 1).

Continue reading "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 arcsin(x) = arcsin(2x\(\sqrt{1 - x^{2}}\)) or, 2 sin\(^{-1}\) x = sin\(^{-1}\) (2x\(\sqrt{1 - x^{2}}\))

Continue reading "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 arccos(x) - arccos(y) = arccos(xy + \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))

Continue reading "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 - \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))

Continue reading "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 arcsin (x) - arcsin(y) = arcsin (x \(\sqrt{1 - y^{2}}\) - y\(\sqrt{1 - x^{2}}\))

Continue reading "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 arccot(x) - arccot(y) = arccot(\(\frac{xy + 1}{y - x}\)) (i.e., cot\(^{-1}\) x + cot\(^{-1}\) y = cot\(^{-1}\)

Continue reading "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\(^{-1}\)

Continue reading "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 arcsin (x) + arcsin(y) = arcsin (x \(\sqrt{1 - y^{2}}\) + y\(\sqrt{1 - x^{2}}\))

Continue reading "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 arctan(x) + arctan(y) + arctan(z) = arctan\(\frac{x + y + z – xyz}{1 – xy – yz – zx}\) (i.e., tan\(^{-1}\) x

Continue reading "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(\(\frac{x - y}{1 + xy}\)) (i.e., tan\(^{-1}\) x - tan\(^{-1}\) y

Continue reading "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 = tan\(^{-1}\)

Continue reading "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 arcsec(x) + arccsc(x) = \(\frac{π}{2}\) (i.e., sec\(^{-1}\) x + csc\(^{-1}\) x = \(\frac{π}{2}\)).

Continue reading "arcsec x + arccsc x = π/2 | arcsec(x) + arccsc(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 = \(\frac{π}{2}\)).

Continue reading "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 arcsin(x) + arccos(x) = \(\frac{π}{2}\). Proof: Let, sin\(^{-1}\) x = θ Therefore, x = sin θ

Continue reading "arcsin x + arccos x = π/2 | arcsin(x) + arccos(x) = \(\frac{π}{2}\) | Examples"

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.

Continue reading "General and Principal Values of cot\(^{-1}\) x | Inverse Circular Functions"

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.

Continue reading "General and Principal Values of sec\(^{-1}\) x | General values of arc sec x"

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.

Continue reading "General and Principal Values of csc\(^{-1}\) 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.

Continue reading "General and Principal Values of tan\(^{-1}\) 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.

Continue reading "General and Principal Values of cos\(^{-1}\) x | Inverse Circular Functions"

What are the general and principal Values of sin\(^{-1}\) x? What is sin\(^{-1}\) ½? We know that sin (30°) = ½.

Continue reading "General and Principal Values of sin\(^{-1}\) x | Inverse Trigonometric Functions"

We will discuss here about Inverse trigonometric Functions or inverse circular functions. The inverse of a function f: A ⟶B exists if and only if f is one-one onto (i.e., bijection) and given by

Continue reading "Inverse Trigonometric Functions | Inverse Circular Functions | Introduction"

We will learn how to find the general solution of trigonometric equation of various forms using the identities and the different properties of trig functions.

Continue reading "General solution of Trigonometric Equation |Solution of a Trigonometric Equation"

We will learn how to solve different types of problems on trigonometric equation containing one or many trig functions. First we need to solve the trigonometric function (if required) and

Continue reading "Problems on Trigonometric Equation | Trigonometric Equation Formulas"

We will learn how to solve trigonometric equation using formula. Here we will use the following formulas to get the solution of the trigonometric equations. (a) If sin θ = 0 then θ = nπ

Continue reading "Trigonometric Equation using Formula | Problems on Trigonometric Equation"

How to find the general solution of the equation cos θ = 0? Prove that the general solution of cos θ = 0 is θ = (2n + 1) π/2, n ∈ Z

Continue reading "Cos Theta Equals 0 | General Solution of the Equation cos θ = 0 | cos θ = 0"

How to find the general solution of an equation of the form tan θ = tan ∝? Prove that the general solution of tan θ = tan ∝ is given by θ = nπ +∝, n ∈ Z.

Continue reading "Tan Theta Equals Tan Alpha | General Solution of tan θ = tan ∝ |General Solution"

How to find the general solution of an equation of the form cos θ = cos ∝? Prove that the general solution of cos θ = cos ∝ is given by θ = 2nπ ± ∝, n ∈ Z.

Continue reading "Cos Theta Equals Cos Alpha | General Solution of cos θ = cos ∝ |General Solution"

How to find the general solution of the equation tan θ = 0? Prove that the general solution of tan θ = 0 is θ = nπ, n ∈ Z.

Continue reading "Tan Theta Equals 0 | General Solution of the Equation tan θ = 0 | tan θ = 0"

How to find the general solution of the equation sin θ = 0? Prove that the general solution of sin θ = 0 is θ = nπ, n ∈ Z Solution:

Continue reading "Sin Theta Equals 0 | General Solution of the Equation sin θ = 0 | sin θ = 0"

How to find the general solution of an equation of the form sin θ = 1? Prove that the general solution of sin θ = 1 is given by θ = (4n + 1)π/2, n ∈ Z.

Continue reading "Sin Theta Equals 1 | General Solution of the Equation sin θ = 1 | sin θ = 1"

Trigonometric equations of the form a cos theta plus b sin theta equals c (i.e. a cos θ + b sin θ = c) where a, b, c are constants (a, b, c ∈ R) and |c| ≤ √(a^2 + b^2 ).

Continue reading "a cos Theta Plus b sin Theta Equals c |General Solution of a cos θ + b sin θ = c"

How to find the general solution of an equation of the form sin θ = sin ∝? Prove that the general solution of sin θ = sin ∝ is given by θ = nπ + (-1)^n ∝, n ∈ Z.

Continue reading "Sin Theta Equals Sin Alpha | General Solution of sin θ = sin ∝ |General Solution"

We will discuss about the trigonometric equation formula. We need to use the formula to find the general solution or some particular solution of different types of trigonometric equation.

Continue reading "Trigonometric Equation Formula | General Solution | Particular Solution "

How to find the general solution of an equation of the form cos θ = -1? Prove that the general solution of cos θ = -1 is given by θ = (2n + 1)π, n ∈ Z.

Continue reading "Cos Theta Equals Minus 1 |General Solution of the Equation cos θ = -1|cos θ = -1"

How to find the general solution of an equation of the form cos θ = 1? Prove that the general solution of cos θ = 1 is given by θ = 2nπ, n ∈ Z.

Continue reading "Cos Theta Equals 1 | General Solution of the Equation cos θ = 1 | cos θ = 1"

How to find the general solution of an equation of the form sin θ = 1? Prove that the general solution of sin θ = 1 is given by θ = (4n + 1)π/2, n ∈ Z.

Continue reading "Sin Theta Equals Minus 1 |General Solution of the Equation sin θ = -1|sin θ = -1"

**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.**

## 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.