Class 10th Math Formula

A class 10th math formula helps students to solve questions easily. It provides them with a quick revision and can help them prepare for competitive exams. It is prepared chapter-wise and contains examples to make it easier for students to understand concepts and apply formulas. This helps students build their confidence and achieve better results in exams.

Trigonometric formulas

The class 10th mathematics curriculum often requires students to learn and apply trigonometric formulas. These formulas can help solve many different types of problems, including those related to the sign of angles in different quadrants, Pythagorean identities, and product identities. There are also numerous applications of trigonometry, including in satellite navigation systems.

Trigonometric ratios are relationships between angles and lengths. They are based on the three sides of a right triangle. These sides are called the hypotenuse, the base, and the height. The angles in the triangle are called the angles th. It is important to understand the different trigonometric ratios and how they relate to each other. There are two major systems of trigonometric formulas: trigonometric identities and trigonometric ratios.

The six basic trigonometric ratios are the sine, cosine, tangent, and secant. In addition, there are several useful trigonometric identities that can be used in expressions. Trigonometric identities are useful for figuring out the value of an angle, and are useful for solving equations with trigonometric functions.

Class 10 math formulas can be used in many practical situations, such as building parallel walls and inclined roofs, fixing tiles, and more. They are also useful in statistics and probability calculations, which are used to analyze census data and calculate insurance risks. Therefore, it is imperative to know the formulas and how to apply them correctly to solve these problems.

Algebraic formulas

Algebra is a branch of mathematics that deals with variables and the rules for manipulating those symbols. Students studying Algebra Class 10th must have a firm grasp on the algebraic formulas to succeed in the subject. The quadratic formula is an example of such a formula, which students can use to find the values of a variable. A determinant is also a useful tool in finding the nature of a root.

Algebraic formulas can be used in solving equations, evaluating functions and solving problems in algebra. Students should remember these formulas before the examinations so that they can use them when they need to. While learning the algebraic formulas, students should not rely on rote learning. They should also learn how to apply them to various problems.

Another important concept in algebra is the laws of exponents. These laws apply to any non-zero integer. For example, 6x = x – 2. The next step is to divide an algebraic expression by eliminating common factors. This is a skill that can be applied to any kind of mathematics.

A student who knows how to apply the basic principles of algebra can solve equations. It is a powerful tool that can help students solve problems, calculate unknown numbers, and identify conditions with both static and dynamic components. There are three different types of algebra, namely, elementary algebra, advanced algebra, and commutative algebra.

During class 10, students must learn the basic algebraic formulas. They must also study polynomials. This will help them in solving complex equations. Besides, they should learn about the use of variables and factors in algebra. For instance, students should learn how to simplify complex equations by factoring them.

Besides being important for the class 10th board exam, the formulas students learn in this class are important for many other subjects. They are used in medicine, finance, engineering, and architecture. Almost every industry employs them in some form or another. In short, students who learn algebraic formulas are well equipped to handle a wide range of situations, including daily tasks and real-life situations.

A good way to learn algebraic formulas for class 10th is to learn them chapter-by-chapter. For example, a formula that contains two like terms and one unlike term is called a trinomial. This type of equation emphasizes the use of addition, subtraction, and multiplication. Like terms have similar numerical coefficients while differences are equal.

Statistics formulas

In class 10th math, statistics is one of the most important subjects. Students should know how to calculate the mean, median, and mode of grouped data. These concepts will be useful in higher classes and competitive examinations. They should also be aware of the formulas used in mensuration questions.

The use of these formulas will be very important in the analysis of data and the calculation of probability. They are also important in calculating different measures of central tendency, dispersion, and correlation. These measures are useful for testing hypotheses and drawing conclusions based on data. The mean is calculated by dividing the number of observations by their median and mode. The median and mode values are the middle and most frequently occurring values in a series.

Class 10 math formulas are extremely important for the preparation of high school and college entrance examinations. Students who memorize them tend to score higher marks and do better on math exams. These formulas are the foundation of advanced math studies, and help students to solve complex problems in a faster and easier manner.

Class 10 math formulas are important because they are used in a variety of occupations and fields. These include medicine, architecture, finance, engineering, and computer science. They are also used in practically every business today. As a result, class 10 math formulas are important and are essential for a variety of careers.

trigonometry formulas

 त्रिकोणमिति क्या है | What is Trigonometry in Hindi त्रिकोणमिति गणित की एक ऐसी शाखा है जिसके अंतर्गत त्रिभुज की भुजाओं और कोणों के बीच के संबंधों का अध्ययन करते है. त्रिकोणमिति पूरे ज्यामिति में पाई जाती है, क्योंकि प्रत्येक सीधी-पक्षीय आकृति को त्रिभुजों के संग्रह के रूप में तोड़ा जा सकता है. इसके अलावा, त्रिकोणमिति गणित की अन्य शाखाओं, विशेष रूप से जटिल संख्याओं, अनंत श्रृंखला, लघुगणक और कलन के साथ आश्चर्यजनक रूप से जटिल संबंध रखती हैं.

 दरअसल Trigonometry ग्रीक के दो शब्दों से मिलकर बना है, जिसे निम्न प्रकार परिभाषित किया जाता है: Trigonon  – जिसका अर्थ तीन कोण (Tri-angles) होता है. Metron – इसका अर्थ मापना  (Measurement) होता है. ये त्रिकोणमितिय शब्द 16वीं सदी का लैटिन व्युत्पन्न है, जो त्रिभुज (ट्रिग्नॉन) और माप (मेट्रॉन) के लिए ग्रीक शब्दों से लिया गया है. दुसरें शब्दों में, त्रिकोणमिति किसे कहते है? यह गणित की वह शाखा है जिसमे त्रिभुज के भुजाओं की लम्बाई तथा उनके कोणों के बीच स्थापित सम्बन्ध की व्याख्या करता है, उसे त्रिकोणमिति कहते है.

 आमतौर पर त्रिकोणमिति में उपयोग किए जाने वाले कोण के 6 होते हैं,

 जो इस प्रकार है: त्रिकोणमिति फलनसंक्षिप्त रूपSine (ज्या)SinCosine (कोज्या )CosTangent (स्पर्शज्या)TanCo-secant  (व्युज्या)CosecSecant (व्युकोज्या)SecCo-tangent (व्युस्पर्शज्या)Cot त्रिकोणमिति के सभी सूत्र | All Trigonometry Formula in Hindi Trikonmiti फार्मूला का प्रयोग त्रिभुज के तीनों भुजाओं को मापने के लिए किया जाता है. एक समकोण त्रिभुज में, तीन भुजाएँ होती है जिसका नाम कर्ण, लम्ब और आधार होता है.

किसी भी Trikonmiti Formula निरूपण निम्न कथन से किया जाता है: “एक समकोण त्रिभुज में, कर्ण का वर्ग त्रिभुज के अन्य दो पक्षों के वर्गों के योग के बराबर होता है.” समकोण त्रिभुज की भुजाओ की परिभाषा निम्न प्रकार होती है: कर्ण: 90° के सामने वाली भुजा को समकोण कहा जाता है. लम्ब: वैसी भुजा जो आधार के साथ 90 डिग्री का कोण बनाती हैं, उसे लम्ब कहा जाता है. आधार: समकोण त्रिभुज में शेष भुजा को आधार कहा जाता है. त्रिकोणमिति के सामान्य फार्मूला |


Basic Trigonometry Formula गणित में त्रिकोणमिति के 6 फलनों का अध्ययन विशेष रूप से किया जाता है, जो त्रिभुज के भुँजाओं एवं कोणों को मापने में मदद करता है. इसके उपरांत सभी फार्मूला प्रयोग में आते है.


 sinθ = लम्ब/कर्ण = p / h cosθ = आधार/कर्ण = b / h tanθ = लम्ब/आधार = p / b cotθ = आधार/लम्ब = b / p secθ = कर्ण/आधार = h / b coescθ = कर्ण/लम्ब = h / p त्रिकोणमितिय अनुपातों के बिच सम्बन्ध sin, cos, tan, sec, cosec, और cot ये सभी समकोण त्रिभुज के भुजाओं एवं कोणों के मापने में सबसे प्रमुख किरदार निभाते है.

इसलिए, इनके संबंधो के विषय में जानकारी भी एक फार्मूला है. जिसका प्रयोग कर प्रश्न हल किया जाता है. हालांकि, यह प्राथमिक इकाई है लेकिन ये फार्मूला सबसे अहम् होते है. जो इस प्रकार है.

sinθ × Cosecθ = 1

sinθ = 1 / Cosecθ

Cosecθ = 1 / sinθ

Cosθ × Secθ = 1

Cosθ = 1 / Secθ

Secθ = 1 / Cosθ

Tanθ × Cotθ = 1

Tanθ = 1 / Cotθ

Cotθ = 1 / Tanθ 

Tanθ = sinθ / Cosθ

Cotθ = Cosθ / sinθ

महत्वपूर्ण त्रिकोणमिति सूत्र इस त्रिकोणमिति सूत्र का प्रयोग ज्यादातर प्रश्न हल करने के लिए होता है, जिसे याद करना आवश्यक है.

Sin θ / Cos θ = Tan

 θ Cos θ / Cot θ = Sin θ

 Cot θ / Cosec θ = Cos θ

 Cosec θ / Sec θ = Cot θ

Sec θ / Tan θ = Cosec

θ Tan θ  / Sin θ  = Sec θ


  1. (α+в)²= α²+2αв+в²
  2. (α+в)²= (α-в)²+4αв
  3. (α-в)²= α²-2αв+в²
  4. (α-в)²= (α+в)²-4αв
  5. α² + в²= (α+в)² – 2αв.
  6. α² + в²= (α-в)² + 2αв.
  7. α²-в² =(α + в)(α – в)
  8. 2(α² + в²) = (α+ в)² + (α – в)²
  9. 4αв = (α + в)² -(α-в)²
  10. αв ={(α+в)/2}²-{(α-в)/2}²
  11. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
  12. (α + в)³ = α³ + 3α²в + 3αв² + в³
  13. (α + в)³ = α³ + в³ + 3αв(α + в)
  14. (α-в)³=α³-3α²в+3αв²-в³
  15. α³ + в³ = (α + в) (α² -αв + в²)
  16. α³ + в³ = (α+ в)³ -3αв(α+ в)
  17. α³ -в³ = (α -в) (α² + αв + в²)
  18. α³ -в³ = (α-в)³ + 3αв(α-в)

ѕιη0° =0

ѕιη30° = 1/2

ѕιη45° = 1/√2

 ѕιη60° = √3/2

 ѕιη90° = 1

¢σѕ ιѕ σρρσѕιтє σƒ ѕιη

 тαη0° = 0

тαη30° = 1/√3

тαη45° = 1

 тαη60° = √3

тαη90° = ∞

¢σт ιѕ σρρσѕιтє σƒ тαη

ѕє¢0° = 1

ѕє¢30° = 2/√3

ѕє¢45° = √2

ѕє¢60° = 2

ѕє¢90° = ∞

¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢

  1. ѕιη2α = 2ѕιηα¢σѕα
  2. ¢σѕ2α = ¢σѕ²α − ѕιη²α
  3. ¢σѕ2α = 2¢σѕ²α − 1
  4. ¢σѕ2α = 1 − ѕιη²α
  5. 2ѕιη²α = 1 − ¢σѕ2α
  6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²
  7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)²
  8. тαη2α = 2тαηα / (1 − тαη²α)
  9. ѕιη2α = 2тαηα / (1 + тαη²α)
  10. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)
  11. 4ѕιη³α = 3ѕιηα − ѕιη3α
  12. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α
  13. ѕιη²Θ+¢σѕ²Θ=1
  14. ѕє¢²Θ-тαη²Θ=1
  15. ¢σѕє¢²Θ-¢σт²Θ=1

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