Find the best tutors and institutes for Class 10 Tuition
Q1:
Express the trigonometric ratios $\sin A$, $\sec A$ and $\tan A$ in terms of $\cot A$.
Solution :
Given: The trigonometric ratios $\sin A$, $\sec A$, and $\tan A$.
To Find: Express $\sin A$, $\sec A$, and $\tan A$ in terms of $\cot A$.
Step 1: Expressing $\tan A$ in terms of $\cot A$
By the definition of reciprocal trigonometric identities, we know that the tangent ratio is the reciprocal of the cotangent ratio.
Formula: $\tan A = \frac{1}{\cot A}$
Thus, $\tan A = \frac{1}{\cot A}$.
Step 2: Expressing $\sin A$ in terms of $\cot A$
We use the trigonometric identity relating $\csc A$ and $\cot A$: $1 + \cot^2 A = \csc^2 A$.
Taking the square root on both sides: $\csc A = \sqrt{1 + \cot^2 A}$.
Since $\sin A = \frac{1}{\csc A}$ [Reciprocal identity], we substitute the expression for $\csc A$:
$\sin A = \frac{1}{\sqrt{1 + \cot^2 A}}$
Step 3: Expressing $\sec A$ in terms of $\cot A$
We use the trigonometric identity relating $\sec A$ and $\tan A$: $1 + \tan^2 A = \sec^2 A$.
Substitute the expression for $\tan A$ found in Step 1 ($\tan A = \frac{1}{\cot A}$):
$\sec^2 A = 1 + \left(\frac{1}{\cot A}\right)^2$
$\sec^2 A = 1 + \frac{1}{\cot^2 A}$
Find a common denominator:
$\sec^2 A = \frac{\cot^2 A + 1}{\cot^2 A}$
Taking the square root on both sides:
$\sec A = \sqrt{\frac{\cot^2 A + 1}{\cot^2 A}}$
$\sec A = \frac{\sqrt{1 + \cot^2 A}}{\cot A}$
Final Answer:
$\sin A = \frac{1}{\sqrt{1 + \cot^2 A}}$
$\sec A = \frac{\sqrt{1 + \cot^2 A}}{\cot A}$
$\tan A = \frac{1}{\cot A}$
More Questions from Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.3
- Q2: Write all the other trigonometric ratios of $\angle A$ in terms of $\sec A$.
- Q3(i): Choose the correct option. Justify your choice. (i) $9 \sec^2 A – 9 \tan^2 A =$
- Q3(ii): Choose the correct option. Justify your choice. (ii) $(1 + \tan \theta + \sec \theta) (1 + \cot \theta – \text{cosec } \theta) =$
- Q3(iii): Choose the correct option. Justify your choice. (iii) $(\sec A + \tan A) (1 – \sin A) =$
- Q3(iv): Choose the correct option. Justify your choice. (iv) $\frac{1 + \tan^2 A}{1 + \cot^2 A} =$
- Q4(i): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) $(\text{cosec } \theta – \cot \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}$
- Q4(ii): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ii) $\frac{\cos A}{1 + \sin A} + \frac{1 + \sin A}{\cos A} = 2 \sec A$
- Q4(iii): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iii) $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \text{cosec } \theta$ [Hint : Write the expression in terms of $\sin \theta$ and $\cos \theta$]
- Q4(iv): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) $\frac{1 + \sec A}{\sec A} = \frac{\sin^2 A}{1 – \cos A}$ [Hint : Simplify LHS and RHS separately]
- Q4(ix): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ix) $(\text{cosec } A – \sin A) (\sec A – \cos A) = \frac{1}{\tan A + \cot A}$ [Hint : Simplify LHS and RHS separately]
- Q4(v): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (v) $\frac{\cos A – \sin A + 1}{\cos A + \sin A – 1} = \text{cosec } A + \cot A$, using the identity $\text{cosec}^2 A = 1 + \cot^2 A$.
- Q4(vi): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vi) $\sqrt{\frac{1 + \sin A}{1 – \sin A}} = \sec A + \tan A$
- Q4(vii): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vii) $\frac{\sin \theta - 2 \sin^3 \theta}{2 \cos^3 \theta - \cos \theta} = \tan \theta$
- Q4(viii): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (viii) $(\sin A + \text{cosec } A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$
- Q4(x): Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (x) $(\frac{1 + \tan^2 A}{1 + \cot^2 A}) = (\frac{1 - \tan A}{1 - \cot A})^2 = \tan^2 A$
CBSE Solutions for Class 10 Mathematics Introduction to Trigonometry
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Introduction to Trigonometry
Nanmangalam, Chennai
3 yrs of
Exp
2 students
88 hrs of classes completed
260
per hour
Online Classes
Tutor's home
Hi, my name is M.Praveshika. I am a graduate in Master of Philosophy (Mathematics) from Stella Maris College. During my degree, I have developed an easy algorithm for solving certain graphs in my specialization paper. I spent my spare time by tutoring my cousins and working with them gave me a new understanding how students are facing problems in understanding the concepts. So i started my career as a Subject Matter Expert (EzeeScore) which enabled me to utilize my skills and knowledge for the growth of the students as well as to the organisation. My key skills are Leadership, Time maganement, Decision making and Problem solving.
Top Tutor
Talwandi Sector-B, Kota
10 yrs of
Exp
1 student
699 hrs of classes completed
1850
per hour
Online Classes
Tutor's home
My teaching exp.11 year in most reputed coaching in india. Mentor of jee top rank air-12 yatis agrawal, 19, 28 many more in top 100 in jee adavnced. Many of students got 100%tile in jee mains along with 100% marks in board exams. I also provide complete relevent study material like worksheet, practice sheet , dpps , assignment etc. Daily quizz based on assignment. Periodically test papers topic wise, minor and major as per shedule. I have helped thousands of students overcome their fear of maths.
Top Tutor
Ashok Vihar, Gurgaon
10 yrs of
Exp
1 student
221 hrs of classes completed
350
per hour
Online Classes
With a strong academic foundation in Mathematics, including an M.Sc. in Mathematics, B.Sc., BTC, and CTET qualification, I am a dedicated Mathematics educator committed to helping students build conceptual clarity, logical reasoning, and analytical problem-solving skills. I have been successfully teaching Mathematics for over 12 years through my coaching institute in Gurgaon, while also conducting engaging online classes for students across India and internationally. I teach students across CBSE, ICSE, NIOS, and State Boards, adapting my teaching methodology to suit each curriculum and the individual learning needs of every student. My teaching approach focuses on simplifying complex mathematical concepts through structured lesson planning, personalised instruction, continuous assessment, and interactive learning techniques. I believe every student can excel in Mathematics with the right guidance, consistent practice, and a strong conceptual foundation. I also specialise in Vedic Mathematics, helping students significantly improve calculation speed, accuracy, mental agility, and confidence in school, competitive, and entrance examinations. As an UrbanPro Super Tutor, I am recognised for consistently delivering high-quality teaching and maintaining excellent student and parent satisfaction. Over the years, I have helped hundreds of students achieve outstanding academic results while developing confidence and a genuine interest in Mathematics. My passion for teaching, commitment to academic excellence, and student-centred approach enable me to create an engaging, motivating, and result-oriented learning environment where every learner can achieve their highest potential. If you are looking for a dedicated and experienced Mathematics tutor who can help you achieve excellent results and build strong fundamentals, I invite you to book a demo class today. Let’s work together to make Mathematics simple, enjoyable, and rewarding for you!
Top Tutor
Sector 19, Noida
3 yrs of
Exp
12 students
615 hrs of classes completed
Online Classes
• 3+ years of teaching experience. • teaching online tuitions of Mathematics for Class 10-12th. • pursued M.Sc. Mathematics from University of Delhi & B.Sc. Mathematical Sciences from University of Delhi. Passionate about solving mathematical problems and I have helped many students to overcome the fear of Maths.
Im so grateful that i got in contact with palak ma'am in my difficult phase.. my boards are on the end and she is standing with me to support me and help me till the end..thanks alot will make her proud for sure !! amazing teacher !! grateful
Super Tutor
Saheed Nagar, Bhubaneswar
11 yrs of
Exp
36 students
644 hrs of classes completed
499
per hour
Online Classes
▪️Class 10 Board Specialist ▪️IGCSE / IB / CBSE / ICSE / Focus ▪️Syllabus-Aligned Teaching ▪️Concept Clarity First ▪️Exam-Oriented Preparation ▪️Board Pattern Mastery ▪️Previous Year Questions Practice ▪️Structured Lesson Planning ▪️Step-by-Step Problem Solving ▪️Time Management Training ▪️Weekly Tests & Mock Exams ▪️Performance Tracking ▪️Targeted Weak Area Support ▪️Answer Writing Techniques ▪️Regular Parent Updates ▪️Result-Driven Approach
An excellent Maths tutor who combines strong subject knowledge with a clear and patient teaching approach. He has helped my daughter develop a much better understanding of concepts and, importantly, greater confidence in solving problems. His dedication, regular guidance, and personalised attention are truly commendable. Highly recommended for students looking for a sincere and effective Maths teacher.
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 8.3 worksheets
Download Now
