Class 10 Maths Chapter 8 Solutions PDF Download
Are you looking for a reliable and easy way to prepare for your Class 10 Maths exam? Do you want to learn the concepts of trigonometry and solve the problems with confidence? If yes, then you have come to the right place. In this article, we will provide you with everything you need to know about Class 10 Maths Chapter 8 - Introduction to Trigonometry. You will get to know how to download the PDF of NCERT Solutions for Class 10 Maths Chapter 8, what are the trigonometry formulas for Class 10 Maths Chapter 8, and what are the important questions for Class 10 Maths Chapter 8. So, without further ado, let's get started.
Introduction to Trigonometry
What is trigonometry and why is it important?
Trigonometry is the branch of mathematics that deals with the relationships between angles, lengths, and heights of triangles. It is derived from two Greek words, 'trigonon' meaning triangle and 'metron' meaning measure. Trigonometry is important because it helps us to find distances, heights, angles, and areas of various shapes and objects. It also has applications in various fields like engineering, physics, astronomy, navigation, surveying, etc.
class 10 maths chapter 8 solutions pdf download
What are the main topics covered in Chapter 8 of Class 10 Maths?
Chapter 8 of Class 10 Maths introduces you to the basics of trigonometry. It covers the following topics:
Trigonometric ratios: These are the ratios of the sides of a right-angled triangle with respect to one of its acute angles. There are six trigonometric ratios, namely sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).
Trigonometric identities: These are the equations that involve trigonometric ratios and are true for all values of the angles. The most basic trigonometric identity is sinθ + cosθ = 1.
Trigonometric ratios of specific angles: These are the values of trigonometric ratios for some standard angles like 0, 30, 45, 60, and 90.
Trigonometric ratios of complementary angles: These are the relationships between trigonometric ratios of two angles whose sum is 90. For example, sin (90 - θ) = cos θ.
NCERT Solutions for Class 10 Maths Chapter 8
How to download the PDF of NCERT Solutions for Class 10 Maths Chapter 8?
If you want to download the PDF of NCERT Solutions for Class 10 Maths Chapter 8, you can follow these simple steps:
Go to [BYJU'S website](^1^) and search for NCERT Solutions for Class 10 Maths.
Select Chapter 8 - Introduction to Trigonometry from the list of chapters.
You will see a page with all the exercises and examples of Chapter 8 of Class 10 Maths.
Click on the exercise or example that you want to view or download.
You will see the detailed and step-by-step solution of each question on the screen.
To download the PDF of the solution, click on the download icon on the top right corner of the page.
You can also print or share the PDF of the solution with your friends or teachers.
Alternatively, you can also use this [direct link] to download the PDF of NCERT Solutions for Class 10 Maths Chapter 8.
* NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry PDF Download
* How to Download Free PDF of NCERT Solutions for Class 10 Maths Chapter 8
* CBSE Class 10 Maths Chapter 8 Trigonometry Solutions PDF Download
* Toppr NCERT Solutions for Class 10 Maths Chapter 8 Free PDF Download
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* Class 10 Maths Chapter 8 Trigonometric Ratios and Identities Solutions PDF Download
* NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1 PDF Download
* NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 PDF Download
* NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3 PDF Download
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What are the benefits of using NCERT Solutions for Class 10 Maths Chapter 8?
NCERT Solutions for Class 10 Maths Chapter 8 are very helpful for students who want to ace their exams and score high marks. Some of the benefits of using NCERT Solutions for Class 10 Maths Chapter 8 are:
They are prepared by expert teachers who have years of experience in teaching and solving maths problems.
They are based on the latest CBSE syllabus and exam pattern and follow the NCERT guidelines.
They cover all the concepts and topics of Chapter 8 in a clear and concise manner.
They provide detailed and step-by-step solutions for each question, along with diagrams, formulas, and examples wherever necessary.
They help students to understand the logic and method behind each solution and improve their problem-solving skills.
They also help students to revise the chapter quickly and effectively before the exam.
Trigonometry Formulas for Class 10 Maths Chapter 8
What are the basic trigonometric ratios and identities?
The basic trigonometric ratios are the ratios of the sides of a right-angled triangle with respect to one of its acute angles. They are denoted by sin, cos, tan, cosec, sec, and cot. The following table shows the definitions and values of these ratios for an angle θ in a right-angled triangle ABC, where AB is the opposite side, BC is the adjacent side, and AC is the hypotenuse.
RatioDefinitionValue
sin θOpposite/HypotenuseAB/AC
cos θAdjacent/HypotenuseBC/AC
tan θOpposite/AdjacentAB/BC
cosec θHypotenuse/OppositeAC/AB
sec θHypotenuse/AdjacentAC/BC
cot θAdjacent/OppositeBC/AB
The basic trigonometric identity is an equation that involves trigonometric ratios and is true for all values of the angles. The most basic trigonometric identity is:
sinθ + cosθ = 1
This identity can be derived from the Pythagoras theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is,
AC = AB + BC
If we divide both sides by AC, we get:
(AC/AC) = (AB/AC) + (BC/AC)
1 = (AB/AC) + (BC/AC)
1 = sinθ + cosθ
What are the trigonometric formulas for specific and complementary angles?
The trigonometric formulas for specific angles are the values of trigonometric ratios for some standard angles like 0, 30, 45, 60, and 90. The following table shows these values for each ratio.
Anglesin θcos θtan θcosec θsec θcot θ
0010-1-
301/23/21/322/33
451/21/21221
603/21/232/321/3
9010-1-0
The trigonometric formulas for complementary angles are the relationships between trigonometric ratios of two angles whose sum is 90. For example, sin (90 - θ) = cos θ. The following table shows these formulas for each ratio.
Ratios of (90 - θ)Ratios of θ
sin (90 - θ)cos θ
cos (90 - θ)
sin θ /tr>
tan (90 - θ)
cot θ /tr>
cosec (90 - θ)
sec θ /tr>
sec (90 - θ)
cosec θ /tr>
cot (90 - θ)
tan θ /tr>
/table>
How to solve the important questions for Class 10 Maths Chapter 8?
To solve the important questions for Class 10 Maths Chapter 8, you need to follow these steps:
Read the question carefully and identify the given information and the required answer.
Draw a diagram if possible and label the sides and angles of the triangle.
Use the appropriate trigonometric ratio or identity to form an equation or expression.
Simplify and solve the equation or expression for the unknown value.
Check your answer by substituting it in the original equation or expression.
Write your answer in the correct form and unit.
Here are some examples of how to solve the important questions for Class 10 Maths Chapter 8:
Example 1: Find the value of sin 18 using the trigonometric identity sin 2θ = 2 sin θ cos θ.
Solution:
We can write sin 18 as sin (36/2) and use the identity sin 2θ = 2 sin θ cos θ to get:
sin 18 = sin (36/2) = 2 sin (36/4) cos (36/4)
We know that sin 36 = (5 - 1)/4 and cos 36 = (5 + 1)/4 from the trigonometric ratios of specific angles. Substituting these values, we get:
sin 18 = 2 [(5 - 1)/4] [(5 + 1)/4]
sin 18 = (5 - 1)(5 + 1)/8
sin 18 = (5) - 1/8
sin 18 = (5 - 1)/8
sin 18 = 1/2
Example 2: If tan A = cot B, prove that A + B = 90.
Solution:
We can use the definition of tan and cot to write tan A = cot B as:
tan A = cot B
Opposite/Adjacent = Adjacent/Opposite
Opposite x Opposite = Adjacent x Adjacent
(Opposite) = (Adjacent)
Hypotenuse - (Opposite) = Hypotenuse - (Adjacent)
Hypotenuse(1 - cosA) = Hypotenuse(1 - sinB)
Hypotenuse(sinA) = Hypotenuse(sinB)
sinA = sinB
sin A = sin B
If we assume that both A and B are acute angles, then we can take the positive sign and get:
sin A = sin B
This implies that A and B are either equal or supplementary. But since tan A and cot B are defined only for acute angles, we can rule out the possibility of A and B being equal. Therefore, we have:
A + B = 180 - A
A + A + B = 180
2A + B = 180
A + B = (180 - 90)/2
A + B = 90
Hence, proved.
Example 3: If sin A + sinA = 1, find the value of cosA.
Solution:
We can use the basic trigonometric identity sinA + cosA = 1 to write cosA as:
cosA = 1 - sinA
Substituting the given value of sin A + sinA = 1, we get:
cosA = 1 - (1 - sin A)
cosA = sin A
Hence, the value of cosA is sin A.
Conclusion
Summary of the main points of the article
In this article, we have learned about Class 10 Maths Chapter 8 - Introduction to Trigonometry. We have seen how to download the PDF of NCERT Solutions for Class 10 Maths Chapter 8, what are the trigonometry formulas for Class 10 Maths Chapter 8, and what are the important questions for Class 10 Maths Chapter 8. We have also solved some examples of how to apply the concepts and formulas of trigonometry. We hope that this article has helped you to understand and master trigonometry and prepare well for your exam.
FAQs
Here are some of the frequently asked questions related to Class 10 Maths Chapter 8:
Q: What is the difference between trigonometric ratios and trigonometric functions?
A: Trigonometric ratios are the ratios of the sides of a right-angled triangle with respect to one of its acute angles. Trigonometric functions are the functions that relate an angle to a trigonometric ratio. For example, sin θ is a trigonometric function that gives the value of the sine ratio for any angle θ.
Q: How to remember the trigonometric ratios of specific angles?
A: One way to remember the trigonometric ratios of specific angles is to use a mnemonic device like SOHCAHTOA, which stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent. Another way is to use a table or a diagram that shows the values of the ratios for each angle.
Q: How to prove trigonometric identities?
A: To prove trigonometric identities, we need to use the basic trigonometric identities, formulas, and properties to manipulate and simplify both sides of the equation until they become equal. We can also use substitution, elimination, or verification methods to prove trigonometric identities.
Q: How to find the value of a trigonometric ratio for any angle?
A: To find the value of a trigonometric ratio for any angle, we can use a calculator or a table that gives the values of the ratios for different angles. We can also use the trigonometric formulas for specific and complementary angles to find the values of the ratios for some angles in terms of other angles.
Q: How to solve problems involving trigonometry?
A: To solve problems involving trigonometry, we need to follow these steps:
Read the problem carefully and identify the given information and the required answer.
Draw a diagram if possible and label the sides and angles of the triangle.
Use the appropriate trigonometric ratio or identity to form an equation or expression.
Simplify and solve the equation or expression for the unknown value.
Check your answer by substituting it in the original equation or expression.
Write your answer in the correct form and unit.
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