# All Trigonometry Formulas For Class 12

Class 12 Trigonometry Formula

This formula is based on the comparison of the increase in the number of points for each grade of class 12 from first to 10th.

Firstly, we need to look at what makes class 12 into a class.

It is a class that is known for different awards such as examinations and graduation.

These awards vary from one course to another depending on the changing and existing college structure.

This is based on the reason that they are awarded on the basis of personal motivation, not grades.

Class structure chart

There are other similar classes like life and disability, which all have the same criteria and strength to bring about a successful career and are held differently across different industries.

Let’s analyze the below graph by visualizing its fundamentals.

As we can see, there is a uniform increase in numbers for every grade and so all grades of class 12 must always begin at the first stage and rise steadily in all of them.

The standard formula for class 12

The First will begin by having a class 1 of 12 and the second at 2, three, five, six, and so on.

We can agree that the classes will have the same number of points.

Our state of equations evolves to

Second to 10 will be a class of 12 plus a class of 10 plus a class of 12 plus a class of 10 plus a class of 12 plus a class of 10 plus a class of 12 plus a class of 10 plus a class of 10

Also Read:- All Trigonometry Formula & Identities

List of Trigonometry Formula for Class 12

### Basic Concepts

Here are the domain and range of basic trigonometric functions:

Sine function, sine: R → [– 1, 1]

Cosine function, cos : R → [– 1, 1]

Tangent function, tan : R – { x : x = (2n + 1) π/2, n ∈ Z} →R

Cotangent function, cot : R – { x : x = nπ, n ∈ Z} →R

Secant function, sec : R – { x : x = (2n + 1) π/2, n ∈ Z} →R – (– 1,1)

Cosecant function, cosec : R – { x : x = nπ, n ∈ Z} →R – (– 1, 1)

Properties of Inverse Trigonometric Functions

sin-1 (1/a) = cosec-1(a), a ≥ 1 or a ≤ – 1

cos-1(1/a) = sec-1(a), a ≥ 1 or a ≤ – 1

tan-1(1/a) = cot-1(a), a>0

sin-1(–a) = – sin-1(a), a ∈ [– 1, 1]

tan-1(–a) = – tan-1(a), a ∈ R

cosec-1(–a) = –cosec-1(a), | a | ≥ 1

cos-1(–a) = π – cos-1(a), a ∈ [– 1, 1]

sec-1(–a) = π – sec-1(a), | a | ≥ 1

cot-1(–a) = π – cot-1(a), a ∈ R

Addition Properties of Inverse Trigonometry functions

sin-1a + cos-1a = π/2, a ∈ [– 1, 1]

tan-1a + cot-1a = π/2, a ∈ R

cosec-1a + sec-1a = π/2, | a | ≥ 1

tan-1a + tan-1 b = tan-1 [(a+b)/1-ab], ab<1

tan-1a – tan-1 b = tan-1 [(a-b)/1+ab], ab>-1

tan-1a – tan-1 b = π + tan-1[(a+b)/1-ab], ab > 1; a,b > 0

Twice of Inverse of Tan Function

2tan-1a = sin-1 [2a/(1+a2)], |a| ≤ 1

2tan-1a = cos-1[(1-a2)/(1+a2)], a ≥ 0

2tan-1a = tan-1[2a/(1+a2)], – 1 < a < 1