# Trigonometry All Formulas PDF Download

Trigonometry All Formulas PDF Download, Trigonometry holds an essential place from the point of view of SSC, NDA, CDS, and other competitive exams. Class 10 Trigonometry Formula, Trigonometric Formulas For Class 12 Pdf, If we analyze the question papers of SSC and other competitive exams of the last three or four years, Class 11 Trigonometry Formulas, then we know that trigonometry has three to four questions in SSC (10+2 level, graduation level, and CPO) and other competitive exams. Are being asked.

Trigonometry All Formulas PDF – In today’s Content, we will know all the Trigonometry or Trigonometry formulas  (All Trigonometry formulas in Hindi & English). Questions based on the procedure of trigonometry function are often asked in board exams or competitive exams. Basic and tricky questions based on trigonometry formulas are requested in 9th class, 10th class, 11th class, and 12th class exams.

## Trigonometry Formula

Table of Contents

### Table of Trigonometry Functions (chart)

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## Basic Formulas of Trigonometry

1. sinA = perpendicular hypotenuse
2. cosA = base hypotenuse
3. tanA = perpendicular base
4. cotA = base perpendicular
5. secA = hypotenuse base
6. cosecA = hypotenuse
7. sinA =1 cosecA
8. cosA =1 secA
9. tanA =1 cotA
10. cotA =1 tanA
11. secA =1 cosA
12. cosecA =1 sinA
13. tanA =sinA cosA
14. cotA =cosA sinA
15. sinA x cosecA = 1
16. cosA x secA = 1
17. tanA x cotA = 1
18. sin 2 A + cos 2 A = 1
19.  sec 2 A – tan 2 A = 1
20.  cosec 2 A – cot 2 A = 1

### Formulas for Measurement of Angles in Trigonometry

1. radian measurement = π 180x degree measurement
2. degree measurement = 180 πx radian measurement

### Fundamentals of Trigonometry

1. sin2x + cos2x = 1
2. 1 + tan2x = sec2
3. 1 + cot2x = cosec2
4. cos (2πn + θ) = cosθ
5. sin (2πn + θ) = sinθ
6. sin (-θ) = -sinθ
7. cos (-θ) = cosθ

### Trigonometry ratio of the sum of two angles

1. sin (A + B) = sinA.cosB + cosA.sinB
2. cos (A + B) = cosA.cosB – sinA.sinB
3. tan (A + B) = tanA + tanB 1 – tanA.tanB
4. cot (A + B) = cotA.cotB – 1 cotB + cotA

### More Trigonometry Formula

(A) (1) sin (π 2+ A) = cosA (2) cos (π 2+ A) = -sinA (3) tan (π 2+ A) = -cotA (4) cot (π 2+ A) = -tanA (5) sec (π 2+ A) = -cosecA (6) cosec (π 2+ A) = secA

(B) (1) sin (π + A) = -sinA (2) cos (π + A) = -cosA (3) tan (π + A) = tanA (4) cot (π + A) = cotA ( 5) sec (π + A) = -secA (6) cosec (π + A) = -cosecA

(C) (1) sin (3π 2+ A) = -cosA (2) cos (3π 2+ A) = sinA (3) tan (3π 2+ A) = -cotA (4) cot (3π 2+ A) = -tanA (5) sec (3π 2+ A) = cosecA (6) cosec (3π 2+ A) = -secA

(D) (1) sin (2π + A) = sinA (2) cos (2π + A) = cosA (3) tan (2π + A) = tanA (4) cot (2π + A) = cotA (5) sec (2π + A) = secA (6) cosec (2π + A) = cosecA

### Trigonometry ratio of difference of two angles

(1) sin (A – B) = sinA.cosB – cosA.sinB

(2) cos (A – B) = cosA.cosB + sinA.sinB

(3) tan (A – B) = tanA – tanB 1 + tanA.tanB (4) cot (A – B) = cotA.cotB + 1 cotB – cotA

### More Trigonometry Formula

(A) (1) sin (π 2- A) = cosA (2) cos (π 2- A) = sinA (3) tan (π 2- A) = cotA (4) cot (π 2- A) = tanA (5) sec (π 2- A) = cosecA (6) cosec (π 2- A) = secA

(B) (1) sin (π – A) = sinA (2) cos (π – A) = -cosA (3) tan (π – A) = -tanA (4) cot (π – A) = -cotA (5) sec (π – A) = -secA (6) cosec (π – A) = -cosecA

(C) (1) sin (3π 2- A) = -cosA (2) cos (3π 2- A) = -sinA (3) tan (3π 2- A) = cotA (4) cot (3π 2- A) = tanA (5) sec (3π 2- A) = -cosecA (6) cosec (3π 2- A) = -secA

(D) (1) sin (2π – A) = -sinA (2) cos (2π – A) = cosA (3) tan (2π – A) = -tanA (4) cot (2π – A) = -cotA (5) sec (2π – A) = secA (6) cosec (2π – A) = -cosecA

### Two Formulas of Trigonometry

(1) sin(A + B) sin(A – B) = sin2A – sin2

(2) cos(A + B) cos(A – B) = cos2A – sin2B

### Expressing Trigonometry Ratios of Angle 2A in Terms of Angle A

(1) sin2A = 2sinA.cosB

(2) cos2A = cos 2 A – sin 2 A = 2cos 2 A – 1 = 1 – 2 sin 2 A

(3) tan2A = 2tanA 1 – tan 2 A

(4) sin2A = 2tanA 1 + tan 2 A

(5) cos2A = 1 – tan 2 A 1 + tan 2 A

### Expressing Trigonometry Ratios of Angle 3A in Terms of Angle A

(1) sin3A = 3sinA – 4sin 3A

(2) cos3A = 4cos 3A – 3cosA

(3) tan3A = 3tanA – tan 3 A 1 – 3tan 2 A

### sum or difference of product

(1) 2sinA.cosB = sin (A + B) + sin (A – B)

(2) 2cosA.sinB = sin (A + B) – sin (A – B)

(3) 2cosA.cosB = cos (A + B) + cos (A – B)

(4) 2sinA.sinB = cos (A – B) – cos (A + B)

### Conversion of sum and difference product

(1) sinC + sinD = 2 sinC + D 2cosC – D 2

(2) sinC – sinD = 2 cosC + D 2sinC – D 2

(3) cosC + cosD = 2 cosC + D 2cosC – D 2

(4) cosC – cosD = 2 sinC + D 2sinD – C 2

### General Solution of Simple Trigonometry Equations

(1) If sinθ = 0, then its general solution will be = nπ, where n is zero or any positive or negative integer, that is, n.

(2) If cosθ = 0, its general solution will be = (2n + 1)π/2, where n is zero or any positive or negative integer, that is, n.

(3) If tanθ = 0, then the general solution will be = nπ, where n is zero or any positive or negative integer, that is, n.

### General Solution of Trigonometry Equations

(1) If sinθ = sinα then its comprehensive solution = nπ + (-1) n  α ∀ n ∈ I

(2) If cosθ = cosα then its comprehensive solution = 2nπ + α, ∀ n ∈ I

(3) if tanθ = tanα then its broad solution = nπ + α, n ∈ I

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