# Mathematical Formulas ### Algebra Formulas

1. (a+b =a²+2ab+b²
2. (ab)² =a²2ab+b²
3. (a+b)(ab) =a²b²
4. (x+a)(x+b) =x²+(a+b)x+ab
5. (x+a)(xb) =x²+(ab)xab
6. (xa)(x+b) =x²+(ba)xab
7. (xa)(xb) =x²(a+b)x+ab
8. (a+b =a³+b³+3ab(a+b)
9. (ab)³ =a³b³3ab(ab)
10. (x+y+z)² =x²+y²+z²+2xy+2yz+2xz
11. (x+yz)² =x²+y²+z²+2xy2yz2xz
12. (xy+z)² =x²+y²+z²2xy2yz+2xz
13. (xyz)² =x²+y²+z²2xy+2yz2xz
14. x³+y³+z³3xyz =(x+y+z)(x²+y²+z²xyyzxz)
15. x²+y² =12[(x+y)²+(xy)²]
16. (x+a)(x+b)(x+c) =x³+(a+b+c)x²+(ab+bc+ca)x+abc
17. x³+y³ =(x+y)(x²xy+y²)
18. x³y³ =(xy)(x2+xy+y2)
19. x²+y²+z²xyyzzx =12[(xy)²+(yz)²+(zx)²]

### Coordinate Geometry

• Distance Formulae: Consider a line having two points A(x1, y1) and B(x2, y2), then the distance of these points is given as:
• Section Formula: If a point p divides a line AB with coordinates A(x1, y1) and B(x2, y2), in ratio m:n, then the coordinates of the point p are given as:
• Mid Point Formula: The coordinates of the mid-point of a line AB with coordinates A(x1, y1) and B(x2, y2), are given as:
• Area of a Triangle: Consider the triangle formed by the points A(x1, y1) and B(x2, y2) and C(x3, y3) then the area of a triangle is given as-

### Circles

Important properties related to circles:

• Equal chord of a circle are equidistant from the centre.
• The perpendicular drawn from the centre of a circle, bisects the chord of the circle.
• The angle subtended at the centre by an arc = Double the angle at any part of the circumference of the circle.
• Angles subtended by the same arc in the same segment are equal.
• To a circle, if a tangent is drawn and a chord is drawn from the point of contact, then the angle made between the chord and the tangent is equal to the angle made in the alternate segment.
• The sum of opposite angles of a cyclic quadrilateral is always 180o.

Important formulas related to circles:

Area of a Segment of a Circle: If AB is a chord which divides the circle into two parts, then the bigger part is known as major segment and smaller one is called minor segment Circle with segment

Here, Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB

### Trigonometry Formulas

In a right-angled triangle, the Pythagoras theorem states
(perpendicular )+ ( base )2 = ( hypotenuse )2

Important trigonometric properties: (with P = perpendicular, B = base and H = hypotenuse)

• SinA = P / H
• CosA = B / H
• TanA = P / B
• CotA = B / P
• CosecA = H / P
• SecA = H/B

Trigonometric Identities:

• sin2A + cos2A=1
• tan2A +1 = sec2A
• cot2A + 1= cosec2A

Relations between trigonometric identities are given below:

Trigonometric Ratios of Complementary Angles are given as follows:

• sin (90° – A) = cos A
• cos (90° – A) = sin A
• tan (90° – A) = cot A
• cot (90° – A) = tan A
• sec (90° – A) = cosec A
• cosec (90° – A) = sec A

Values of Trigonometric Ratios of 0° and 90° are tabulated below:

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