# IMP Formula | Basic | Trigonometry | Derivatives | Integration PDF

In Engineering and Technology formula plays main role, because without formulas no feature studies possible in science and technology. Formula is a compressed way of expressing information in symbols, as in a mathematical formula or a science formula. In this article some IMP Formula are listed below.

## Laws of Indices

Multiplication

1. am x an = amxn
2. (a x b)n=an x bn

Division

1. am / an=am-n
2. (a / b)n = an / b

Other

1. (a x m)n = amxn
2. 1 / an = a-n
3. a0 = 1

## Factorization and Expansion

This list of formulas are use when we want to factorized some variable or to expand variables.

1. a– b2 = (a + b) (a – b)
2. a+ b2 = (a + b)2 – 2ab
3. a– b= (a – b) (a+ ab + b2)
4. a+ b= (a + b) (a– ab + b2)
5. a4 – b= (a– b2 ) ( a+ b2 )
6. (a + b)= a+ 2ab + b2
7. (a − b)= a− 2ab + b2
8. (a + b)3 =a+ b+ 3ab(a + b)
9. (a – b)= a– b– 3ab(a – b)
10. (a + b)4 = a+ 4a3b + 6a2b2 + 4ab3 + b4
11. (a − b)4 = a4 − 4a3b + 6a2b2 − 4ab3 + b4
12. (a + b + c)2 = a2 + b2 +c2 + 2ab + 2ac + 2bc

## Trigonometry IMP Formula

### Basic Trigonometric Function Formula

By using a right-angled triangle as a reference, we can find all trigonometry term values.

1. sin θ = Opposite Side/Hypotenuse
2. cos θ = Adjacent Side/Hypotenuse
3. tan θ = Opposite Side/Adjacent Side
4. cot θ = Adjacent Side/Opposite Side
5. sec θ = Hypotenuse/Adjacent Side
6. cosec θ = Hypotenuse/Opposite Side

### Reciprocal Identities

1. cosec θ = 1/sin θ
2. sec θ = 1/cos θ
3. cot θ = 1/tan θ
4. sin θ = 1/cosec θ
5. cos θ = 1/sec θ
6. tan θ = 1/cot θ

### Trigonometry Table

 Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360° Angles (In Radians) 0° 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 ∞ csc ∞ 2 √2 2/√3 1 ∞ -1 ∞ sec 1 2/√3 √2 2 ∞ -1 ∞ 1

### Periodicity Identities (in Radians) formulas

These IMP formula are used to shift the angles by θ

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

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

sin (3π/2 – A)  = – cos A & cos (3π/2 – A)  = – sin A

sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A

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

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

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

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

### Co-function Identities (in Degrees) formulas

1. sin (90°−x) = cos x
2. cos (90°−x) = sin x
3. tan (90°−x) = cot x
4. cot (90°−x) = tan x
5. sec (90°−x) = csc x
6. csc (90°−x) = sec x

### Sum & Difference Identities

1. sin (x+y) = sin(x) cos(y) + cos(x) sin(y)
2. cos (x+y) = cos(x) cos(y) – sin(x) sin(y)
3. tan (x+y) = (tan x + tan y) / (1−tan x •tan y)
4. sin (x–y) = sin(x) cos(y) – cos(x) sin(y)
5. cos (x–y) = cos(x) cos(y) + sin(x) sin(y)
6. tan (x−y) = (tan x–tan y) / (1+tan x • tan y)

### Double Angle Identities

sin (2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]

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

cos (2x) = 2cos2(x) − 1 = 1–2sin2(x)

tan (2x) = [2tan(x)] / [1−tan2(x)]

sec (2x) = secx / (2-sec2 x)

csc (2x) = (sec x. csc x)/2

### Triple Angle Identities

1. sin 3x = 3sin x – 4sin3x
2. cos 3x = 4cos3x-3cos x
3. tan 3x = [3tanx-tan3x] / [1-3tan2x]

## IMP Formula PDF

1. Law of Indices
2. Logic of Power and Roots
3. Law of Logarithams
4. Factorization
5. Expansion
6. Trigonometry
7. Trigonometry Factorization
8. Trigonometry Identities
9. De-Factorization
11. Trigonometry Ratio of Negative angle
12. Double angle Formula
13. Triple angle Formula
14. Derivatives
15. Integration

### Derivatives

Video lectures of Applied mathematics for Diploma Engineering Students are available on ours Official YouTube Channel Open Mind Guruji.

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