RD Sharma Solutions for Class 11 Maths Chapter 7 – Values of Trigonometric Functions at Sum or Difference of Angles are available here for easy reference. In this chapter, students will learn how to derive formulas that express trigonometric function values at the sum or difference of two angles in terms of their individual values.
The solutions are prepared in a clear and simple manner, making it easier for students to understand key concepts and formulas. These step-by-step solutions follow the latest CBSE syllabus and can be downloaded in PDF format for offline practice.
RD Sharma Solutions Class 11 Maths -Trigonometric Ratios Of Compound Angles Question with Answers
Q1. Find sin(75°) using the sum formula.
Solution: sin(75°) = sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (1/√2)(√3/2) + (1/√2)(1/2) = (√3 + 1)/(2√2)
Q2. Evaluate cos(15°).
Solution: cos(15°) = cos(45° – 30°) = (1/√2)(√3/2) + (1/√2)(1/2) = (√3 + 1)/(2√2)
Q2. Prove that sin(60° + 30°) = 1.
Solution: sin(90°) = 1
Q4. Find tan(75°) using tan(A+B) formula.
Solution: tan75° = tan(45° + 30°) = (1 + 1/√3) / (1 – 1/√3)
Q5. Simplify sin(105°).
Solution: sin105° = sin(60° + 45°) = (√6 + √2)/4
Q6. Express sin(A+B) in terms of sinA, sinB, cosA, cosB.
Solution: sin(A+B) = sinAcosB + cosAsinB
Q7. Express cos(A–B) in terms of sin and cos.
Solution: cos(A–B) = cosAcosB + sinAsinB
Q8. Evaluate cos(75°) using sum formula.
Solution: cos75° = (√3 – 1)/(2√2)
Q9. Find tan(15°).
Solution: tan15° = (1 – 1/√3)/(1 + 1/√3)
Q10. Simplify sin(120°).
Solution: sin120° = √3/2
Q11. Find cos(120°).
Solution: cos120° = -1/2
Q12. Prove sin(180° – A) = sinA.
Solution: Identity holds true
Q13. Prove cos(180° – A) = –cosA.
Solution: Identity holds true
Q14. Show tan(180° + A) = tanA.
Solution: Identity holds true
Q15. Simplify sin(225°).
Solution: sin225° = –1/√2
Q16. Find cos(330°).
Solution: cos330° = √3/2
Q17. Evaluate sin(15°) using subtraction formula.
Solution: sin15° = (√3 – 1)/(2√2)
Q18. Find tan(105°).
Solution: tan105° = (√3 + 1)/(1 – √3)
Q19. Prove sin(A+B)sin(A–B) = sin²A – sin²B.
Solution: Identity holds true
Q20. Simplify cos(300°).
Solution: cos300° = 1/2
Q21. Prove sinAcosB = ½[sin(A+B) + sin(A–B)].
Solution: Identity holds true
Q22. Evaluate tan(225°).
Solution: tan225° = 1
Q23. Find sin(390°).
Solution: sin390° = sin30° = 1/2
Q24. Prove cos(360° – A) = cosA.
Solution: Identity holds true
Q25. Simplify sin(270° – A).
Solution: sin(270° – A) = –cosA
RD Sharma Solutions Class 11 Maths Chapter 7 Download Free PDF
Frequently Asked Questions
Chapter 7 focuses on the Values of Trigonometric Functions at Sum or Difference of Angles. It helps students learn formulas to calculate the sine, cosine, and tangent of compound angles (A + B or A - B) using individual angle values.
There are three exercises in Chapter 7, each designed to explain the derivation and application of compound angle formulas through step-by-step problem-solving.
Compound angle formulas are crucial for simplifying trigonometric expressions and solving problems involving angle sums or differences. They are frequently used in higher mathematics, competitive exams like JEE, and real-life applications in physics and engineering.
Chapter 7 covers key identities like:
sin(A ± B) = sinAcosB ± cosAsinB
cos(A ± B) = cosAcosB ∓ sinAsinB
tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)
Yes, RD Sharma solutions are very helpful as they provide step-by-step explanations, helping students strengthen their basics and perform well in school exams and entrance tests.
Yes, many educational websites like Infinity Learn, Vedantu, BYJU’S, and other CBSE-focused platforms offer free downloadable PDF solutions for RD Sharma Class 11 Chapter 7.
Practicing from RD Sharma is a great start. To master compound angles, it is advisable to:
- Practice regularly
- Solve previous years' papers
- Understand the derivations, not just memorize formulas
Common angles include 0°, 30°, 45°, 60°, 90°, and their sums or differences like 75°, 15°, 105°, etc., for which standard trigonometric values are applied.