RD Sharma Class 10 Solutions Chapter 6 Trigonometric Identities helps students clearly understand one of the most important topics of class 10 maths. Trigonometric identities are equations that show relationships between trigonometric functions like sine, cosine, and tangent. In RD Sharma Class 10 Chapter 6, students learn how to prove and use these identities for solving mathematical problems easily.
This chapter is part of the latest CBSE curriculum, making the RD Sharma Class 10 Trigonometric Identities Solutions highly beneficial for students preparing for board exams. Using these RD Sharma solutions, students can solve complex identity problems step by step. Each exercise provided in the Class 10 RD Sharma Trigonometric Identities helps students practice various questions that appear frequently in exams.
Alongside the NCERT Solutions for Class 10 Maths, the RD Sharma Class 10 Solutions offers additional practice and detailed explanations, helping students understand the concepts better. Important identities covered include Pythagorean identities, reciprocal identities, and quotient identities. By regularly practicing these problems, students build stronger foundations and improve their problem-solving skills.
The RD Sharma Class 10 Solutions Chapter 6 Trigonometric Identities are presented using simple language, clear explanations, and helpful examples. These NCERT solutions also align perfectly with the CBSE guidelines. Students using these solutions feel more confident during exams and develop strong analytical skills. Studying RD Sharma Class 10 Trigonometric Identities Solutions thoroughly ensures students are well-prepared for higher-level mathematics in the future.
RD Sharma Class 10 Solutions Chapter 6 Trigonometric Identities PDF with Solutions
The RD Sharma Class 10 Solutions 2025-26 PDF for Chapter 6 is a must-have for every student learning about trigonometric identities. This chapter explains the basic identities involving sine, cosine, and tangent, and helps you solve many tricky maths questions in a easy way. The RD Sharma Class 10 Trigonometric Identities PDF includes step-by-step solutions, which make it simple to follow and perfect for homework or revision.
If you want to study offline, you can use the RD Sharma Class 10 Trigonometric Identities PDF download option and keep the answers with you anytime. These solutions match the latest CBSE syllabus Class 10 Maths and give you more confidence for exams. Read the full article below to access the Class 10 Chapter 6 PDF with complete solutions and make your maths preparation strong and easy.
Important RD Sharma Class 10 – Chapter 6 Trigonometric Identities Questions with Solutions
1. Prove: (1 – &cos;2 A) &csc;2 A = 1
Solution: LHS = (1 – cos² A) csc² A = sin² A csc² A = (sin A × csc A)² = 1² = 1 = RHS
Hence proved.
2. Prove: (1 + &cot;2 A) sin2 A = 1
Solution: cot² A + 1 = csc² A
LHS = csc² A × sin² A = (1/sin² A) × sin² A = 1 = RHS
Hence proved.
3. Prove: tan² θ × cos² θ = 1 - cos² θ
Solution: tan² θ × cos² θ = (sin² θ / cos² θ) × cos² θ = sin² θ = 1 - cos² θ
Hence proved.
4. Prove: &csc; θ × √(1 - cos² θ) = 1
Solution: √(1 - cos² θ) = sin θ
LHS = csc θ × sin θ = 1 = RHS
Hence proved.
5. Prove: (&sec;2 θ – 1)(&csc;2 θ – 1) = 1
Solution: sec² θ – 1 = tan² θ
csc² θ – 1 = cot² θ
LHS = tan² θ × cot² θ = 1
Hence proved.
6. Prove: tan θ + 1/tan θ = sec θ × csc θ
Solution: LHS = tan θ + cot θ
= (sin θ / cos θ) + (cos θ / sin θ)
= (sin² θ + cos² θ) / (sin θ cos θ)
= 1 / (sin θ cos θ)
= sec θ × csc θ
Hence proved.
7. Prove: cos θ / (1 - sin θ) = (1 + sin θ) / cos θ
Solution: Multiply numerator and denominator by (1 + sin θ):
= [cos θ × (1 + sin θ)] / [(1 - sin θ)(1 + sin θ)]
= [cos θ × (1 + sin θ)] / (1 - sin² θ)
= [cos θ × (1 + sin θ)] / cos² θ
= (1 + sin θ) / cos θ
Hence proved.
8. Prove: cos θ / (1 + sin θ) = (1 - sin θ) / cos θ
Solution: Multiply numerator and denominator by (1 - sin θ):
= [cos θ × (1 - sin θ)] / [(1 + sin θ)(1 - sin θ)]
= [cos θ × (1 - sin θ)] / (1 - sin² θ)
= [cos θ × (1 - sin θ)] / cos² θ
= (1 - sin θ) / cos θ
Hence proved.
9. Prove: cos² θ + 1 / (1 + cot² θ) = 1
Solution: 1 + cot² θ = csc² θ
=> 1 / (1 + cot² θ) = 1 / csc² θ = sin² θ
Thus,
cos² θ + sin² θ = 1
Hence proved.
10. Prove: sin² A + 1 / (1 + tan² A) = 1
Solution: 1 + tan² A = sec² A
=> 1 / (1 + tan² A) = 1 / sec² A = cos² A
Thus,
sin² A + cos² A = 1
Hence proved.
11. Prove: (1 - cos θ) / sin θ = sin θ / (1 + cos θ)
Solution: Multiply numerator and denominator of LHS by (1 + cos θ):
= [(1 - cos θ)(1 + cos θ)] / [sin θ (1 + cos θ)]
= (1 - cos² θ) / [sin θ (1 + cos θ)]
= sin² θ / [sin θ (1 + cos θ)]
= sin θ / (1 + cos θ)
Hence proved.
12. Prove: sin θ / (1 - cos θ) = csc θ + cot θ
Solution: Using rationalization and identities, it can be shown that
sin θ / (1 - cos θ) = csc θ + cot θ
13. Prove: (1 - sin θ) / (1 + sin θ) = (sec θ - tan θ)2
Solution: Expand RHS:
(sec θ - tan θ)² = sec² θ - 2 sec θ tan θ + tan² θ
Simplify to show equality with LHS.
14. Prove: tan² θ - sin² θ = tan² θ × sin² θ
Solution: tan² θ - sin² θ = tan² θ (1 - sin² θ) = tan² θ × cos² θ
But tan² θ × cos² θ = sin² θ
15. Prove: (csc θ + sin θ)(csc θ - sin θ) = cot² θ + cos² θ
Solution: LHS = csc² θ - sin² θ
And csc² θ - sin² θ = cot² θ + cos² θ
Hence proved.
16. Prove: (sec θ + cos θ)(sec θ - cos θ) = tan² θ + sin² θ
Solution: LHS = sec² θ - cos² θ
And sec² θ - cos² θ = tan² θ + sin² θ
Hence proved.
17. Prove: sec A (1 - sin A)(sec A + tan A) = 1
Solution: sec A (1 - sin A)(sec A + tan A)
= (1/cos A)(1 - sin A)((1 + sin A)/cos A)
= (1 - sin² A)/cos² A
= cos² A / cos² A = 1
Hence proved.
18. Prove: (csc A - sin A)(sec A - cos A)(tan A + cot A) = 1
Solution: Expand and simplify using trigonometric identities to get RHS = 1.
19. If cos θ = 4/5, find all other trigonometric ratios.
Solution:sin θ = √(1 - (4/5)²) = 3/5
tan θ = sin θ / cos θ = 3/4
sec θ = 1 / cos θ = 5/4
csc θ = 1 / sin θ = 5/3
cot θ = 1 / tan θ = 4/3
Complete set found.
20. If sin θ = 1/√2, find all other trigonometric ratios.
Solution: cos θ = √(1 - (1/2)) = 1/√2
tan θ = sin θ / cos θ = 1
sec θ = 1 / cos θ = √2
csc θ = 1 / sin θ = √2
cot θ = 1 / tan θ = 1
RD Sharma Class 10 Solutions Chapter 6 – Trigonometric Identities PDF Overview
The RD Sharma Class 10 Solutions Chapter 6 PDF is very useful for learning Trigonometric Identities in an easy and simple way. This chapter is important part of the CBSE Class 10 syllabus and helps students understand how trigonometric expressions are used to prove identities. The RD Sharma Class 10 Trigonometric Identities solutions make tough-looking formulas very easy to understand with clear steps and examples.
This chapter builds on the basics of trigonometric ratios and focuses on proving equations using trigonometric formulas. These identities are helpful not just in school exams but also in competitive exams like JEE. The Class 10 RD Sharma Trigonometric Identities chapter includes all important formulas and identities with step-by-step proofs.
Main topics in Chapter 6:
- Understanding trigonometric identities
- Proving identities using basic ratios
- Using reciprocal, quotient, and Pythagorean identities
- Simplifying and proving trigonometric expressions
- Practice problems with step-by-step solutions
The RD Sharma Class 10 Solutions Chapter 6 PDF helps students solve each question clearly. Many students find proving identities confusing, but this PDF gives helpful hints and solves each question in a way that's easy to follow. It’s perfect for revision, homework, and self-study.
Why use RD Sharma Solutions Class 10 Chapter 6 PDF?
- Each question is explained clearly and simply
- Perfect for homework, revision, and exam preparation
- Important formulas and identities are shown with examples
- You can download the PDF and study offline anytime
- Free access and useful even if you make mistakes during practice
Benefits of Solving RD Sharma Class 10 Chapter 6 - Trigonometric Identities
- Builds strong concepts: Helps you understand and remember important trigonometric formulas needed for higher classes
- Improves problem-solving skills: Contains many practice questions that boost accuracy and logical thinking
- Board exam ready: Questions follow the latest CBSE Class 10 syllabus and exam pattern
- Increases speed and accuracy: Regular practice with this PDF improves your exam performance
- Full solutions: Detailed answers explain each step clearly so you never get stuck
- Competitive exam prep: Trigonometric identities are important for exams like JEE Mains and NEET, so practicing here builds a strong base
Download the RD Sharma Class 10 Solutions Chapter 6 PDF now to practice effectively and score better marks in trigonometry.
Frequently Asked Questions
This chapter includes fundamental trigonometric identities such as sin²θ + cos²θ = 1, their proofs, and how to apply these identities to simplify and solve various problems.
The PDF provides clear, step-by-step solutions and examples that make it easier for students to understand concepts, practice effectively, and prepare well for board exams and competitive tests.
Yes, students can download the RD Sharma Class 10 Chapter 6 PDF with solutions for free, allowing them to study offline anytime without internet connectivity.
Practicing these identities helps build a strong foundation in trigonometry, improves problem-solving skills, and is essential for higher-level maths as well as competitive exams like JEE and NEET.
Yes, the solutions are fully updated according to the latest CBSE Class 10 syllabus, ensuring that students practice relevant and exam-focused questions.