Question

Can anyone help me in learning trigonometric identities of class 12th.​

Answer 1

Answer:

Here is the list of formulas for trigonometry.

Basic Formulas

Reciprocal Identities

Trigonometry Table

Periodic Identities

Co-function Identities

Sum and Difference Identities

Double Angle Identities

Triple Angle Identities

Half Angle Identities

Product Identities

Sum to Product Identities

Inverse Trigonometry Formulas

Step-by-step explanation:

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.