Class 12 Maths Ex 2.2 Q2 | Inverse Trigonometric Functions | NCERT Solutions

In this video, we will solve **Question 2 of Exercise 2.2 from Class 12 Maths Chapter 2 – Inverse Trigonometric Functions**, according to the NCERT Mathematics syllabus. This video is designed for students who want to understand NCERT Class 12 Maths solutions step by step and prepare effectively for their CBSE Class 12 Mathematics Board Examination. 📚 *Question Covered in This Video:* Prove that 3 cos⁻¹ x = cos⁻¹ (4x³ − 3x), where x ∈ [1/2, 1]. In this video, I have explained the proof using the triple-angle identity of cosine and the properties of inverse trigonometric functions. The solution focuses on the correct substitution, simplification of the expression, and the importance of the principal value range. *Topics Covered:* Class 12 Maths Chapter 2: Inverse Trigonometric Functions NCERT Exercise 2.2 Question 2 solution Proof of an inverse trigonometric identity Triple-angle formula: cos 3θ = 4 cos³ θ − 3 cos θ Substitution method in inverse trigonometric functions Principal value branch of cos⁻¹ x Step-by-step NCERT Maths solution Important concepts for CBSE Class 12 Maths Board Exams 🎯 *Why Should You Watch This Video?* If you are studying Class 12 Mathematics and find inverse trigonometric identities difficult, this video will help you understand how to approach this type of proof. The solution demonstrates how a suitable substitution can simplify a complicated expression and how the domain restriction ensures that the identity is valid. This question is useful for practising trigonometric identities, inverse trigonometric functions, and mathematical proof-writing techniques. Understanding the method will also help you solve similar NCERT questions independently. 📖 *Who Should Watch This Video?* This video is useful for: Class 12 Maths students CBSE Board Examination preparation NCERT Class 12 Mathematics learners Students revising Chapter 2, Inverse Trigonometric Functions Students practising Exercise 2.2 questions Students looking for short, step-by-step Maths solutions ⏱️ *Video Timestamps* 00:00 Introduction and Question 2 00:25 Understanding the Given Identity 00:50 Applying the Substitution x = cos θ 01:20 Using the Triple-Angle Formula 02:00 Simplification and Verification 02:40 Final Proof and Conclusion 📌 *Watch More on Pie Factor* Subscribe to *Pie Factor* for Class 12 Maths NCERT solutions, exercise-wise explanations, important mathematical identities, and chapter-wise preparation videos. Our goal is to make Mathematics easier to understand through clear explanations and step-by-step solutions. If you find this video helpful, please LIKE the video, SHARE it with your classmates, and SUBSCRIBE to Pie Factor for more NCERT Mathematics solutions. #class12maths #inversetrigonometricfunctions #ncertsolutions #exercise22