 # Trigonometry Formulas For Class 12

Trigonometry Formulas for Class 12: Trigonometry is a branch of Mathematics, that involves the study of the relationship between angles and lengths of triangles. In Class 12 Maths, we come across a different aspect of trigonometry, which is inverse trigonometric functions. Here, we will learn the domain and range of trigonometric functions. The basic trig functions are sin, cos, tan, cot, sec and cosec.

## List Class 12 Trigonometry Formulas

CBSE Class 12 mathematics contains Inverse Trigonometric Functions. This chapter includes definition, graphs and elementary properties of inverse trigonometric functions. Trigonometry formulas for class 12 play a critical role in these chapters. Hence, all trigonometry formulas are provided here.

### 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

These are important formulas introduced in Inverse trigonometric functions chapter of Class 12. Students can solve the problems based on these properties taking reference from this article. To get more formulas, visit us at BYJU’S.

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