NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry - Chapter 8 of NCERT explains the relation between the angles and sides of a right angle triangle. Students appearing in the Class 10 Board exams must check the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry. These Class 10 Maths chapter 8 NCERT solutions are strictly based on the NCERT books for Class 10 Maths. NCERT Class 10 maths solutions chapter 8 gives a detailed explanation of each and every question given in the textbook. Moreover, NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry offers many tips and tricks to solve the questions in an easy way. You can also check the NCERT solutions for Class 10 for other subjects as well.
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NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry Excercise: 8.1
Q1 In , right-angled at , . Determine :
Answer:
We have,
In , B = 90, and the length of the base (AB) = 24 cm and length of perpendicular (BC) = 7 cm
So, by using Pythagoras theorem,
Therefore,
AC = 25 cm
Now,
(i)
(ii) For angle C, AB is perpendicular to the base (BC). Here B indicates to Base and P means perpendicular wrt angle C
So,
and
Answer:
We have, PQR is a right-angled triangle, length of PQ and PR are 12 cm and 13 cm respectively.
So, by using Pythagoras theorem,
Now, According to question,
=
= 5/12 - 5/12 = 0
Answer:
Suppose ABC is a right-angled triangle in which and we have
So,
Let the length of AB be 4 unit and the length of BC = 3 unit
So, by using Pythagoras theorem,
units
Therefore,
and
Answer:
We have,
It implies that In the triangle ABC in which . The length of AB be 8 units and the length of BC = 15 units
Now, by using Pythagoras theorem,
units
So,
and
Q5 Given calculate all other trigonometric ratios.
Answer:
We have,
It means the Hypotenuse of the triangle is 13 units and the base is 12 units.
Let ABC is a right-angled triangle in which B is 90 and AB is the base, BC is perpendicular height and AC is the hypotenuse.
By using Pythagoras theorem,
BC = 5 unit
Therefore,
Q6 If and are acute angles such that , then show that .
Answer:
We have, A and B are two acute angles of triangle ABC and
According to question, In triangle ABC,
Therefore, A = B [angle opposite to equal sides are equal]
Q7 If evaluate:
Answer:
Given that,
perpendicular (AB) = 8 units and Base (AB) = 7 units
Draw a right-angled triangle ABC in which
Now, By using Pythagoras theorem,
So,
and
Answer:
Given that,
ABC is a right-angled triangle in which and the length of the base AB is 4 units and length of perpendicular is 3 units
By using Pythagoras theorem,
In triangle ABC,
AC = 5 units
So,
Put the values of above trigonometric ratios, we get;
LHS RHS
Q9 In triangle , right-angled at , if find the value of:
Answer:
Given a triangle ABC, right-angled at B and
According to question,
By using Pythagoras theorem,
AC = 2
Now,
Therefore,
Q10 In , right-angled at , and . Determine the values of
Answer:
We have, PR + QR = 25 cm.............(i)
PQ = 5 cm
and
According to question,
In triangle PQR,
By using Pythagoras theorem,
PR - QR = 1........(ii)
From equation(i) and equation(ii), we get;
PR = 13 cm and QR = 12 cm.
therefore,
Q11 State whether the following are true or false. Justify your answer.
(i) The value of is always less than 1.
(ii) for some value of angle A.
(iii) is the abbreviation used for the cosecant of angle A.
(iv) is the product of cot and A.
(v) for some angle
Answer:
(i) False,
because , which is greater than 1
(ii) TRue,
because
(iii) False,
Because abbreviation is used for cosine A.
(iv) False,
because the term is a single term, not a product.
(v) False,
because lies between (-1 to +1) [ ]
NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry Excercise: 8.2
Answer:
As we know,
the value of ,
Answer:
..................(i)
It is known that the values of the given trigonometric functions,
Put all these values in equation (i), we get;
Answer:
.....................(i)
We know the values of-
By substituting all these values in equation(i), we get;
Q2 Choose the correct option and justify your choice :
Answer:
Put the value of tan 30 in the given question-
The correct option is (A)
Q2 Choose the correct option and justify your choice :
Answer:
The correct option is (D)
We know that
So,
Q2 Choose the correct option and justify your choice :
is true when =
Answer:
The correct option is (A)
We know that
So,
Q2 Choose the correct option and justify your choice :
Answer:
Put the value of
The correct option is (C)
Q3 If and find
Answer:
Given that,
So, ..........(i)
therefore, .......(ii)
By solving the equation (i) and (ii) we get;
and
Q4 State whether the following are true or false. Justify your answer.
The value of increases as increases.
The value of increases as increases.
for all values of .
is not defined for
Answer:
(i) False,
Let A = B =
Then,
(ii) True,
Take
whent
= 0 then zero(0),
= 30 then value of is 1/2 = 0.5
= 45 then value of is 0.707
(iii) False,
(iv) False,
Let = 0
(v) True,
(not defined)
NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry Excercise: 8.3
Q1 Evaluate :
Answer:
We can write the above equation as;
By using the identity of
Therefore,
So, the answer is 1.
Q1 Evaluate :
Answer:
The above equation can be written as ;
.........(i)
It is known that,
Therefore, equation (i) becomes,
So, the answer is 1.
Q1 Evaluate :
Answer:
The above equation can be written as ;
....................(i)
It is known that
Therefore, equation (i) becomes,
So, the answer is 0.
Q1 Evaluate :
Answer:
This equation can be written as;
.................(i)
We know that
Therefore, equation (i) becomes;
= 0
So, the answer is 0.
Answer:
We have,
and we know that
therefore,
A = 90 - B
A + B = 90
Hence proved.
Q5 If , where is an acute angle, find the value of .
Answer:
We have,
, Here 4A is an acute angle
According to question,
We know that
Q6 If and are interior angles of a triangle , then show that
Answer:
Given that,
A, B and C are interior angles of
To prove -
Now,
In triangle ,
A + B + C =
Hence proved.
Q7 Express in terms of trigonometric ratios of angles between and .
Answer:
By using the identity of and
We know that,
and
the above equation can be written as;
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Excercise: 8.4
Q1 Express the trigonometric ratios and in terms of .
Answer:
We know that
(i)
(ii) We know the identity of
(iii)
Q4 Choose the correct option. Justify your choice.
(A) 1 (B) 9 (C) 8 (D) 0
Answer:
The correct option is (B) = 9
.............(i)
and it is known that
Therefore, equation (i) becomes,
Q4 Choose the correct option. Justify your choice.
(A) 0 (B) 1 (C) 2 (D) –1
Answer:
The correct option is (C)
.......................(i)
we can write his above equation as;
= 2
Q4 Choose the correct option. Justify your choice.
Answer:
The correct option is (D)
..........................eq (i)
The above equation can be written as;
We know that
therefore,
Answer:
We need to prove-
Now, taking LHS,
LHS = RHS
Hence proved.
Answer:
We need to prove-
taking LHS;
= RHS
Hence proved.
[ Hint: Write the expression in terms of and ]
Answer:
We need to prove-
Taking LHS;
By using the identity a ^{ 3 } - b ^{ 3 } =(a - b) (a ^{ 2 } + b ^{ 2 } +ab)
Hence proved.
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
taking LHS;
Taking RHS;
We know that identity
LHS = RHS
Hence proved.
Q5 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. , using the identity
Answer:
We need to prove -
Dividing the numerator and denominator by , we get;
Hence Proved.
Answer:
We need to prove -
Taking LHS;
By rationalising the denominator, we get;
Hence proved.
Q5 Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
Answer:
We need to prove -
Taking LHS;
[we know the identity ]
Hence proved.
Answer:
Given equation,
..................(i)
Taking LHS;
[since ]
Hence proved
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
Answer:
We need to prove,
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
About NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry
Unit 5 "Trigonometry" holds 12 marks out of 80 marks in the maths paper of CBSE board examination and we can expect 2-3 questions from this chapter of total around 8 marks. There is a total of 4 exercises with 27 questions in the NCERT solutions for class 10 maths chapter 8. These NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry are designed to provide assistance for homework and for preparing the board examinations.
The trigonometric ratios of the angle A in right triangle ABC are defined as follows-
The values of all the trigonometric ratios of 0°, 30°, 45°, 60°, and 90° are-
Sin A | 0 | 1 | |||
Cos A | 1 | 0 | |||
Tan A | 0 | 1 | Not defined | ||
Cosec A | Not defined | 2 | 1 | ||
Sec A | 1 | 2 | Not defined | ||
Cot A | Not defined | 1 | 0 |
NCERT Solutions for Class 10 Maths All Chapters
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in Two Variables |
Chapter 4 | NCERT solutions for class 10 maths chapter 4 Quadratic Equations |
Chapter 5 | NCERT solutions for class 10 chapter 5 Arithmetic Progressions |
Chapter 6 | |
Chapter 7 | NCERT solutions for class 10 maths chapter 7 Coordinate Geometry |
Chapter 8 | NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry |
Chapter 9 | NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | NCERT solutions for class 10 chapter maths chapter 12 Areas Related to Circles |
Chapter 13 | NCERT solutions class 10 maths chapter 13 Surface Areas and Volumes |
Chapter 14 | |
Chapter 15 |
Benefits of NCERT Solutions for Class 10 Maths Chapter 8
These Class 10 Maths Chapter 8 NCERT solutions are prepared by the experts. Hence these solutions are 100 per cent reliable.
The NCERT Class 10 maths solutions chapter 8 will be beneficial for Class 10 board exams and for higher studies as well.
These solutions will help in building the basic concepts of trigonometry and bring forth some easy ways to solve the questions.
Subject-wise NCERT Solutions of Class 10
How to use NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry?
Firstly, learn all the concepts given in the NCERT book. Memorise all the trigonometric ratios, angle values, and trigonometric identities.
Now practice exercises by referring to the NCERT Class 10 maths solutions chapter 8.
As the NCERT Solutions for Class 10 Maths Chapter 8 PDF Download is not available. So you can save the webpage to practice the solutions offline.
After doing all these you can practice the last 5 years question papers of board examinations.
Frequently Asked Question (FAQs) - NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry
Question: Whether this unit introduction to trigonometry is helpful for higher studies?
Answer:
Trigonometry is a most important field in mathematics which is useful in almost every field including architecture, electronics, seismology, meteorology, oceanography etc.
Question: How many chapters are there in the class 10 maths?
Answer:
There are a total of 15 chapters in the class 10 maths NCERT.
Question: What book is best for CBSE class 10 maths?
Answer:
NCERT textbook is only book which you should know very well, there is no need of supplementary book as CBSE board class 10 paper is entirely based on the NCERT.
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Questions related to CBSE Class 10th
Board cbse class 10 Is cancelled and promote all student please sir because of corona do not study
Hello aspirant,
No CBSE and ICSE board didn't not cancelled the 10th and 12th exam.
As they had declared that 10th and 12th class exam will not be cancelled and students will have to give it in offline mode in this pandemic also.
Hope this helps you
All the best for your future
CBSE class 10th malayalam can someone please tell me a good one
Hello Dear,
Malayalam is the mother tongue of those who have their roots in Kerala. It is one of the Dravidian languages that has similarities in words with its other contemporary languages such as Tamil and Telugu. People who speak Malayalam are referred to as Mallus. You can download the previous year papers from the link below:
https://school.careers360.com/download/sample-papers/cbse-10th-class-malayalam-solved-sample-paper-2021
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When will the Karnataka NTSE Stage 1 Merit list(i.e people who have cleared stage-1) and the cut off come out?
DSERT, Karnataka has released the NTSE Karnataka 2021 Result stage 1 on March 9, 2021 on their official website ( dsert.kar.nic.in ). It is available in the form of district-wise marks lists , consisting of registration numbers and marks of all students.
Along with the NTSE stage 1 result, cutoff and merit list of selected candidates is also released.
The students those who have cleared the stage 1 exam are eligible to seat for the stage 2 exam which is going to be held on June 13, 2021 . The scholarship will be given to the students who will pass the stage 2 examination.
To know more about NTSE Karnataka Important Dates, Cut-off, Scholarship visit :
https://www.google.com/amp/s/school.careers360.com/articles/ntse-karnataka-result/amp
Hope it helps
Thank You !!!
Age criteria to appear in class 10 CBSE exam
Hello Bishal
According to guidelines of CBSE, minimum age to appear for class x must be 14 years. There is no upper limit to appear for class x cbse board.
A candidate can appear for maximum three attempts.
Some candidates give private exams or sometimes students fail in standard ix then they privately appear for class x then their age must be more than 14 years. Sometimes students appear for x class after one year gap of passing class ix then also their age would be 15 or 16 as there is no upper limit age.
My child is supposed to make another attempt at compartment exam of 10th cbse Missed last date for applying. since the boards are postponed to May 4th can I pay her fees and apply now.
Hello sir I'm sorry to inform you but now you're not eligible to fill the registration form as last date to fill the registration Form was 9th December 2020. Yes examination gets postponed to May but portal to fill the registration form is not open , in case if the registration form portal will open again you can fill the registration form and make the payment.
Feel free to comment if you've any doubt
Good luck