# Trigonometry Formulas PDF – Tricks of Identities, Ratio Table, Functions

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Trigonometry Formulas PDF – Tricks of Identities, Ratio Table, Functions:  What are the important formulas for trigonometry class 10th, class 11, 12, JEE, NDA. We are not writing theory here, only Important formulas and their PDF to download. Or you can download them all as a pdf. You will find all the formulas in a single page.

For class 10th, class 11 and class 12th these trigonometry formulas are key to get more numbers. You can download Trigonometry Formulas PDF and Important formulas pdfs for class 10th, 11th and 12th. But leave them a side and keep practicing with these formulas.

## Trigonometry Formulas PDF – Tricks of Identities, Ratio Table, Functions

Trigonometry: with the help of trigonometry we can calculate angles of right-angle triangle.

There are 6 functions of an angle used in trigonometry and these 6 are as follow.

1. Sine (sin)
2. Cosine (cos)
3. Tangent (tan)
4. Cotangent (cot)
5. Secant (sec)
6. Cosecant (Cosec)

### Basic Trigonometric Function Formulas

Sin θ = Opposite Side/Hypotenuse

Tan θ = Opposite Side/Adjacent Side

Cosec θ = Hypotenuse/Opposite Side

Cot θ = Adjacent Side/Opposite Side ### Reciprocal Identities

Cosec = 1/Sin θ

Sec = 1/Cos θ

Cot = 1/tan θ

Sin = 1/Cosec θ

Cos = 1/Sec θ

Tan = 1/Cot θ ### Trigonometry Table

 Angles (in Degrees) 0º 30º 45º 60º 90º 180º 270º 360º Angles (in Radians) 0º π/6 π/4 π/3 π/2 π 3π/2 2π sin 0 1/2 1/√2 3/2 1 0 -1 0 cos 1 √3/2 1/√2 1/2 0 -1 0 1 tan 0 1/√3 1 √3 ∞ 0 ∞ 0 cot ∞ √3 1 1/√3 0 ∞ 0 ∞ cosec ∞ 2 √2 2/√3 1 ∞ -1 ∞ sec 1 2/√3 √2 2 ∞ -1 ∞ 1 sin (π2 – A) = cos A & cos (π2-A) = sin A

sin (π2 + A)= cos A & cos (π/2 + A) = – sin A

sin (3π2 – A)= -cos A & cos (3π2 – A)= – sin A

sin (3π2 + A)= – cos A & cos (3π2+A) = sin A

sin (π – A) = sin A & cos (π – A) = -cos A

sin (2π – A) = – sin A & cos (π + A) = – cos A

sin (2π – A) = – sin A & cos (2π – A) = cos A

sin (2π + A) = sin & cos (2π + A) = cos A ### Co-function Identities (in Degrees)

Sin (90º – x) = cos x

Cos (90º – x) = sin x

Tan (90º – x) = cot x

Cot (90º – x) = tan x

Sec (90º – x) = csc x

Csc (90º – x) = sec x ### Sum & Difference Identities

Sin (x + y) = sin(x) cos(y) + cos(x) sin(y)

cos (x + y) = cos(x) cos(y) – sin(x) sin(y)

tan (x + y) = (tan x + tan y) / (1-tanx . tan y)

sin (x – y) = sin(x) cos(y) – cos(x) sin(y)

cos (x – y) = cos(x) cos(y) + sin(x) sin(y)

tan (x – y) = (tan x – tan y) / (1+tan x . tan y) ### Double Angle Identities

sin (2x) = 2sin(x) . cos(x) = [2tan x/(tan+tan2 x)]

cos(2x) = cos2 (x) – sin2 (x) = [(1-tan2 x) / (1+tan2 x)]

cos(2x) = 2 cos2 (x) – 1 = 1 – 2 sin2 (x)

tan(2x) = [2tan(x)] / [1-tan2 (x)]

sec (2x) = sec1 x/(2-sec2 x)

csc(2x) = (sec x. csc x)/2 ### Triple Angle Identities

sin 3x = 3 sin x – 4 sin3 x

cos 3x = 4 cos3 x – 3 cos x

sin 3x = 3 sin x – 4 sin3 x

cos 3x = 4 cos3 x – 3 cos x

tan 3x = [3 tan x – tan3 x]/[1 – 3 tan2 x] ### Half Angle Identities ### Product identities

sin x. cos y = sin x + y + sin ⁡(x-y) / 2

Cos x. cos y = sin x+y+cos⁡(x-y) / 2

Sin x. sin y = sin x-y-cos⁡(x-y) / 2

Sin x. sin y = sin x-y-cos⁡(x+y) / 2 ### Sum to Product Identities

Sin x + sin y = 2 sin x+y/2 cos x-y/2

Sin x – sin y = 2 cos x+y/2 sin x-y/2

Cos x + cos y = 2 cos x+y/2 cos x-y/2

Cos x – cos y = – 2 sin x+y/2 sin x-y/2 ### Inverse Trigonometry Formulas

sin-1 (–x) = – sin-1 x

cos-1 (–x) = π – cos-1 x

tan-1 (–x) = – tan-1 x

cosec-1 (–x) = – cosec-1 x

sec-1 (–x) = π – sec-1 x

cot-1 (–x) = π – cot-1 x ### What is Sin 3x Formula?

Sin 3x = 3 sin x – 4 sin3x