Find the best tutors and institutes for Class 10 Tuition
Q11(iv):
State whether the following are true or false. Justify your answer. (iv) $\cot A$ is the product of cot and $A$.
Solution :
Given: The statement "$\cot A$ is the product of $\cot$ and $A$".
To Find: Determine whether the given statement is True or False and provide a mathematical justification.
Step 1: Understanding Trigonometric Notation
In trigonometry, the notation $\cot A$ is a shorthand representation for the "cotangent of the angle $A$". Here, $\cot$ is not a separate algebraic variable or a numerical constant, but rather a functional operator (a trigonometric ratio) that acts upon the argument $A$.
Step 2: Analyzing the Relationship
Let us consider a right-angled triangle $\triangle ABC$ where $\angle B = 90^\circ$ and $\angle A$ is one of the acute angles. By definition, the cotangent of angle $A$ is the ratio of the length of the side adjacent to angle $A$ to the length of the side opposite to angle $A$.
Mathematically, $\cot A = \frac{\text{Adjacent side}}{\text{Opposite side}} = \frac{AB}{BC}$.
Step 3: Evaluating the "Product" Claim
If $\cot A$ were the product of $\cot$ and $A$, then $\cot$ would have to be a value that could be multiplied by $A$. However, $\cot$ by itself has no independent numerical value. It is an operator that requires an angle (the argument) to produce a ratio. If we were to separate them, the expression $\cot$ would be meaningless in the context of geometry and trigonometry.
Step 4: Logical Conclusion
Since $\cot A$ represents a single functional entity where $A$ is the angle associated with the cotangent ratio, it cannot be interpreted as the algebraic product of two distinct factors, $\cot$ and $A$. Therefore, the assertion that $\cot A$ is the product of $\cot$ and $A$ is mathematically incorrect.
Final Answer: False. The term $\cot A$ is a single trigonometric ratio representing the cotangent of angle $A$. The symbol $\cot$ is not a separate variable, and thus $\cot A$ is not the product of $\cot$ and $A$.
More Questions from Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1
- Q1(i): In $\triangle ABC$, right-angled at $B$, $AB = 24$ cm, $BC = 7$ cm. Determine : (i) $\sin A, \cos A$
- Q1(ii): In $\triangle ABC$, right-angled at $B$, $AB = 24$ cm, $BC = 7$ cm. Determine : (ii) $\sin C, \cos C$
- Q10: In $\triangle PQR$, right-angled at $Q$, $PR + QR = 25$ cm and $PQ = 5$ cm. Determine the values of $\sin P, \cos P$ and $\tan P$.
- Q11(i): State whether the following are true or false. Justify your answer. (i) The value of $\tan A$ is always less than 1.
- Q11(ii): State whether the following are true or false. Justify your answer. (ii) $\sec A = \frac{12}{5}$ for some value of angle $A$.
- Q11(iii): State whether the following are true or false. Justify your answer. (iii) $\cos A$ is the abbreviation used for the cosecant of angle $A$.
- Q11(v): State whether the following are true or false. Justify your answer. (v) $\sin \theta = \frac{4}{3}$ for some angle $\theta$.
- Q2: In Fig. 8.13, find $\tan P – \cot R$.
- Q3: If $\sin A = \frac{3}{4}$, calculate $\cos A$ and $\tan A$.
- Q4: Given $15 \cot A = 8$, find $\sin A$ and $\sec A$.
- Q5: Given $\sec \theta = \frac{13}{12}$, calculate all other trigonometric ratios.
- Q6: If $\angle A$ and $\angle B$ are acute angles such that $\cos A = \cos B$, then show that $\angle A = \angle B$.
- Q7(i): If $\cot \theta = \frac{7}{8}$, evaluate : (i) $\frac{(1 + \sin \theta) (1 - \sin \theta)}{(1 + \cos \theta) (1 - \cos \theta)}$
- Q7(ii): If $\cot \theta = \frac{7}{8}$, evaluate : (ii) $\cot^2 \theta$
- Q8: If $3 \cot A = 4$, check whether $\frac{1 - \tan^2 A}{1 + \tan^2 A} = \cos^2 A – \sin^2 A$ or not.
- Q9(i): In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt{3}}$, find the value of: (i) $\sin A \cos C + \cos A \sin C$
- Q9(ii): In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt{3}}$, find the value of: (ii) $\cos A \cos C – \sin A \sin C$
CBSE Solutions for Class 10 Mathematics Introduction to Trigonometry
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Introduction to Trigonometry
Top Tutor
Kharodi West, Mumbai
10 yrs of
Exp
1 student
700
per hour
Student's Home
An accommodating and versatile individual with the talent to develop inspiring hands-on lessons that will capture a child's imagination and breed success.
Super Tutor
Shahdara Chitrakoot, Delhi
10 yrs of
Exp
74 students
3999 hrs of classes completed
750
per hour
Online Classes
With extensive experience in providing Class 10 tuition, I specialize in teaching mathematics, science, and computer science. My approach emphasizes a thorough understanding of key concepts and practical applications. In mathematics, I cover topics such as algebra, geometry, and trigonometry. My science classes include physics, chemistry, and biology, focusing on fundamental principles and real-world relevance. In computer science, I teach programming basics, algorithms, and data management. I use interactive tools, clear presentations, and regular assessments to ensure comprehensive learning. My goal is to build strong foundational knowledge, boost confidence, and prepare students for their board exams and future academic pursuits.
Patient and knowledgeable teacher. Makes difficult maths topics simple and easy. Highly recommend!!!
Top Tutor
Jayanagar, Bangalore
18 yrs of
Exp
28 students
2321 hrs of classes completed
500
per hour
Online Classes
Private teacher. Classes will be taken for science also but only for Physics and Chemistry. I have been teaching for Class 10 for the past 15 years. Focus will be given to each student regarding their difficult concepts. Previous year question papers will be discussed, along with practice worksheets that will be given for each chapter. Coaching will be given to score good marks in respective board exams by giving them tricks to manage the timings
Wonderful teacher with enormous knowledge about the subject with a smile every time while teaching...
Top Tutor
Sector 12, Noida
6 yrs of
Exp
4 students
148 hrs of classes completed
400
per hour
Online Classes
I have worked as PGT teacher in one of the best CBSE schools and all of my students gained more than 90 percent marks. I have full concept of subjects and can assist students in gaining more than 90 percent marks.
Top Tutor
Chitragupta Nagar, Patna Sadar
5 yrs of
Exp
9 students
5038 hrs of classes completed
300
per hour
Online Classes
Hello all, I am Utkarsh kumar. As an experienced, qualified teacher and tutor with over 8 years of experience in teaching Maths, Physics, Chemistry and Biology across different boards including CBSE, and State Board. Passionate about solving mathematical problems and chemical equations. Over the years I have helped thousands of students overcome their fear of Maths, Physics Chemistry and Biology. If u wish to learn in interactive and fun manner, feel free to make a contact.
Find more Tutor for Introduction to Trigonometry in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1 worksheets
Download Now
