Maths( Trigonometry & Algebra) Formulas For Class 10

Maths Formulas For Class 10: Class 10 is one of the most important classes
 in a student’s life. Class 10 board exam result is a deciding factor in selecting the stream for further studies. PCM(physics chemistry mathematics), PCB(physics chemistry biology), & Commerce Maths is one of the most important subjects as it is a basic requirement for a lot of career choices.
Because the concepts covered during this period are asked in various competitive exams, like SSC CGL MTS Railway, CDS, and Rest all even government job exams.

Trigonometry Formulas For Class 10 Maths

The Trigonometric Formulas for Class 10 covers the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).

Let a right-angled triangle ABC is right-angled at point B and have ∠θ$\mathrm{\angle }\theta$ is one of the other two angles.

sin θ = SideoppositetoangleθHypotenuse$\frac{Sideoppositetoangle\theta }{Hypotenuse}$ = PerpendicularHypotenuse$\frac{Perpendicular}{Hypotenuse}$ = P/H

cos θ = AdjacentsidetoangleθHypotenuse$\frac{Adjacentsidetoangle\theta }{Hypotenuse}$ = AdjacentsideHypotenuse$\frac{Adjacentside}{Hypotenuse}$ = B/H

tan θ = SideoppositetoangleθAdjacentsidetoangleθ$\frac{Sideoppositetoangle\theta }{Adjacentsidetoangle\theta }$ = P/B

sec θ = 1cosθ$\frac{1}{cos\theta }$

cot θ = 1tanθ$\frac{1}{tan\theta }$

cosec θ = 1sinθ$\frac{1}{sin\theta }$

tan θ = SinθCosθ$\frac{Sin\theta }{Cos\theta }$

TheTriogonometic Table comprising the values of these trigonometric functions for standard angles is as under:

Angle	0°	30°	45°	60°	90°
sinθ	0	1/2	1/√2	√3/2	1
cosθ	1	√3/2	1/√2	½	0
tanθ	0	1/√3	1	√3	Undefined
cotθ	Undefined	√3	1	1/√3	0
secθ	1	2/√3	√2	2	Undefined
cosecθ	Undefined	2	√2	2/√3	1

Some other trigonometric formulas are given below:

1. sin (90° – θ) = cos θ
2. cos (90° – θ) = sin θ
3. tan (90° – θ) = cot θ
4. cot (90° – θ) = tan θ
5. sec (90° – θ) = cosecθ
6. cosec (90° – θ) = secθ
7. sin2θ + cos2 θ = 1
8. sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
9. Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

Class 10 Maths Formulas For Algebra & Quadratic Equations

To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.

The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:

x=−b±b2−4ac√2a$x=-b\pm \frac{\sqrt{b^2-4ac}}{2a}$

Now you know the basic quadratic equation.

Let us now go through the list of algebra formulas for Class 10:

1. (a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 + b2 – 2ab
3. (a+b) (a-b) = a2 – b2
4. (x + a)(x + b) = x 2 + (a + b)x + ab
5. (x + a)(x – b) = x2 + (a – b)x – ab
6. (a + b)3 = a3 + b3 + 3ab(a + b)
7. (a – b)3 = a3 – b3 – 3ab(a – b)
8. (x – a)(x + b) = x2 + (b – a)x – ab
9. (x – a)(x – b) = x2 – (a + b)x + ab
10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
15. x2 + y2 =½ [(x + y)2 + (x – y)2]
16. (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
17. x3 + y3= (x + y) (x2 – xy + y2)
18. x3 – y3 = (x – y) (x2 + xy + y2)
19. x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]

Quick Note: These formulas will be important in higher classes and various competitive examinations. So, memorize them and understand them well.