Chapter 2 Class 12 Maths NCERT Solutions: Inverse Trigonometric Functions PDF, Free Download

Chapter 2 Class 12 Maths NCERT Solutions: Inverse Trigonometric Functions: Inverse Trigonometric Functions form a crucial part of Class 12 Mathematics and play a key role in calculus, geometry, and mathematical reasoning. Mastering this chapter is important not only for board exams but also for entrance exams like JEE, CUET, and other competitive exams.

To make your preparation easier, we’re providing detailed NCERT Solutions PDF for Chapter 2 – Inverse Trigonometric Functions absolutely free for download.

Key Features of Chapter 2: Inverse Trigonometric Functions Solutions Class 12 – Handwritten Notes

• Subject: Maths (Chapter 2: Inverse Trigonometric Functions)
• Language : Hindi
• Total pages : 26
• File size: 10.8 MB
• Format : PDF
• Well structured and easy to understand
• Includes importance formulas and definitions
• Covers all NCERT syllabus topics
• Useful for quick revision before exam

---

Images of Class 12 Math’s Chapter 2 : Inverse Trigonometric Functions Solutions Free Handwritten Notes PDF

Other Chapters Solutions of Class 12 Maths

Chapter 1 Class 12 Maths NCERT Solutions: Relations and Functions Handwritten Notes PDF Download Free

---

Related Free Notes from Studycart24.com

• Class 12 Business Studies Notes: FREE Notes Chapter 1 to 12
• Complete Class 12 Chemistry Notes PDF with All Chapters for Free
• Class 12 Computer Science Notes PDF in English Free Download
• Class 12 Geography Notes: Download Free PDF of All Chapters in English
• Class 12 Physics Handwritten Notes in English PDF Download
• Class 12 Biology Handwritten Notes PDF Free Download- StudyCart24.com

---

Some Related Notes Links from Amazon Related to Class 12 math’s Handwritten Notes

---

📘 How to Prepare for Chapter 2: Inverse Trigonometric Functions Class 12 Maths

🔍 Step	📚 What to Do	🧠 Tips for Mastery
1. Understand Basic Concepts	Learn about inverse functions, domain, and range.	Use visuals to map original vs inverse functions.
2. Learn Principal Values	Memorize the principal values of all six inverse trig functions.	Create a reference table and revise daily.
3. Study Graphs	Understand how inverse trig functions look graphically.	Sketch graphs repeatedly to memorize shape & range.
4. Practice Properties	Learn and apply identities like: sin⁻¹x + cos⁻¹x = π/2	Practice proof-based questions from NCERT examples.
5. Solve NCERT Exercises	Go through all solved and unsolved questions.	Use step-by-step PDF solutions for clarity.
6. Attempt Miscellaneous Examples	These are often asked in board and JEE exams.	Focus on mixed-type questions for conceptual clarity.
7. Do Previous Year Questions (PYQs)	Solve last 5 years’ questions from this chapter.	Identify pattern and focus areas (domain, range, proof).
8. Practice Daily Revision	Dedicate 15–20 mins daily to revise this chapter.	Keep a formula sheet and graph sketches nearby.
9. Mock Tests & Worksheets	Take chapter-wise mock tests online/offline.	Time yourself and analyze mistakes.
10. Clear Doubts	Ask teachers or friends when stuck.	Use YouTube or math learning apps for visual explanations.

📝 Chapter Included in Our Class 12 Math’s Handwritten Notes PDF

Our Class 12 Maths Handwritten Notes PDF is a complete, exam-ready resource covering every chapter in the CBSE NCERT Syllabus. Each chapter includes theory, solved examples, important formulas, and short tricks to boost your preparation.

📘 Chapter No.	📖 Chapter Name
Chapter 1	Relations and Functions
Chapter 2	Inverse Trigonometric Functions
Chapter 3	Matrices
Chapter 4	Determinants
Chapter 5	Continuity and Differentiability
Chapter 6	Application of Derivatives
Chapter 7	Integrals
Chapter 8	Application of Integrals
Chapter 9	Differential Equations
Chapter 10	Vector Algebra
Chapter 11	Three Dimensional Geometry
Chapter 12	Linear Programming
Chapter 13	Probability

---

🌟 Why Are These Handwritten Notes Special for You?

1. ✅ Neat & Clean Handwriting
   • आसान भाषा और सुंदर लेखन, जिससे समझना और याद रखना आसान हो।
2. ✅ Concept Clarity
   • हर टॉपिक को “क्यों?” और “कैसे?” के साथ समझाया गया है।
3. ✅ Exam-Oriented Content
   • CBSE Board और JEE जैसे एग्जाम्स के हिसाब से महत्वपूर्ण प्रश्न और शॉर्ट ट्रिक्स शामिल हैं।
4. ✅ Chapter-Wise Formula Sheets
   • हर अध्याय के अंत में सभी जरूरी सूत्रों का एक पेज में सारांश।
5. ✅ Useful for Competitive Exams
   • JEE Main, NDA, CUET आदि प्रतियोगी परीक्षाओं के लिए भी उपयोगी।
6. ✅ Well-Labelled Diagrams & Graphs
   • जहां जरूरी है, वहां चार्ट और ग्राफ़ के माध्यम से समझाया गया है।
7. ✅ Time-Saving Revision
   • कम समय में पूरे चैप्टर को कवर करने के लिए संक्षिप्त लेकिन सटीक जानकारी।
8. ✅ Topic-Wise Separation
   • हर टॉपिक को हेडिंग्स, बॉक्स और उदाहरणों के साथ अलग-अलग तरीके से प्रस्तुत किया गया है।
9. ✅ Prepared by Toppers & Experts
   • ये नोट्स अनुभवी शिक्षकों और टॉपर्स की सहायता से तैयार किए गए हैं।
10. ✅ Student-Tested & Approved

• हजारों छात्रों ने इन नोट्स को उपयोगी और प्रभावशाली माना है।

---

🎯 Benefits of Using Handwritten Notes for Class 12 Math’s

1. ✅ Improved Memory Retention
   • Handwritten content is easier to recall due to better cognitive engagement while reading.
2. ✅ Quick & Focused Revision
   • Condensed notes help revise complete chapters quickly before exams.
3. ✅ Better Concept Clarity
   • Concepts are explained in a step-by-step manner, often with real examples and simple language.
4. ✅ Organized & Topic-Wise Structure
   • Topics are neatly arranged with headers, formulas, and boxed highlights — no clutter.
5. ✅ Exam-Ready Content
   • Notes are aligned with CBSE syllabus and include commonly asked board questions and formulas.
6. ✅ Saves Time During Exam Prep
   • No need to search multiple books — everything important is available at one place.
7. ✅ Visual Learning Support
   • Includes graphs, diagrams, and tables that make difficult topics easier to understand.
8. ✅ Boosts Writing & Presentation Style
   • Observing well-written answers improves your own answer-writing skills.
9. ✅ Great for Last-Minute Revision
   • Useful when you need to revise the entire subject in just a few hours.
10. ✅ Portable & Easy to Access

• Download once and use anytime — even offline or as printouts.

---

📘 Class 12 Maths Important Formulae (Quick Glance – Short Form)

📚 Chapter	🔢 Important Formulae
Ch 1: Relations & Functions	No. of Relations=2mn\text{No. of Relations} = 2^{mn}No. of Relations=2mn No. of Functions=nm\text{No. of Functions} = n^mNo. of Functions=nm
Ch 2: Inverse Trig	sin⁡−1x+cos⁡−1x=π2\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}sin−1x+cos−1x=2π​ tan⁡−1x+cot⁡−1x=π2\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2}tan−1x+cot−1x=2π​ tan⁡−1x+tan⁡−1y=tan⁡−1(x+y1−xy)\tan^{-1}x + \tan^{-1}y = \tan^{-1}\left( \frac{x+y}{1-xy} \right)tan−1x+tan−1y=tan−1(1−xyx+y​)
Ch 3: Matrices	(AB)T=BTAT(AB)^T = B^T A^T(AB)T=BTAT (AB)−1=B−1A−1(AB)^{-1} = B^{-1}A^{-1}(AB)−1=B−1A−1
Ch 4: Determinants	( \text{Area} = \frac{1}{2} \left
Ch 5: Continuity & Diff.	ddx(sin⁡x)=cos⁡x\frac{d}{dx}(\sin x) = \cos xdxd​(sinx)=cosx ddx(cos⁡x)=−sin⁡x\frac{d}{dx}(\cos x) = -\sin xdxd​(cosx)=−sinx Chain Rule: dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}dxdy​=dudy​⋅dxdu​
Ch 6: App. of Derivatives	Max/Min via f′(x)f'(x)f′(x), f′′(x)f”(x)f′′(x) Increasing: f′(x)>0f'(x) > 0f′(x)>0 Decreasing: f′(x)<0f'(x) < 0f′(x)<0
Ch 7: Integrals	∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C∫xndx=n+1xn+1​+C ( \int \frac{1}{x} dx = \ln
Ch 8: Area	Area=∫ab[f(x)−g(x)]dx\text{Area} = \int_a^b [f(x) – g(x)] dxArea=∫ab​[f(x)−g(x)]dx
Ch 9: Diff. Equations	Order = Highest Derivative Gen. Solution = Contains C
Ch 10: Vectors	a⃗⋅b⃗=abcos⁡θ\vec{a} \cdot \vec{b} = ab \cos\thetaa⋅b=abcosθ a⃗×b⃗=absin⁡θ n^\vec{a} \times \vec{b} = ab \sin\theta \ \hat{n}a×b=absinθ n^
Ch 11: 3D Geometry	Line: x−x1a=y−y1b=z−z1c\frac{x-x_1}{a} = \frac{y-y_1}{b} = \frac{z-z_1}{c}ax−x1​​=by−y1​​=cz−z1​​ Distance between lines
Ch 12: Linear Programming	Objective: Z=ax+byZ = ax + byZ=ax+by Check values at corner points
Ch 13: Probability	P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) – P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B) ( P(A

---

FAQs on Class 12 Math’s Handwritten Notes PDF Download

---

🧠 Class 12 Math’s Preparation Tips (Short & Effective)

1. ✅ Syllabus जानो – पहले पूरे syllabus और weightage को समझो।
2. 📘 NCERT Strong करो – सारे examples और exercises solve करो।
3. ✍️ Handwritten Notes से पढ़ो – Quick revision के लिए बेहतर हैं।
4. 🧾 Formulas याद रखो – एक formula notebook बनाओ और daily revise करो।
5. 🧮 Daily Practice करो – रोज 5–10 questions अलग-अलग topics से करो।
6. 📄 Previous Year Questions (PYQs) Solve करो – Exam pattern समझने के लिए।
7. ⏱️ Mock Tests दो – हफ्ते में एक बार full syllabus टेस्ट दो।
8. 📐 Concepts समझो, रटने की बजाय – खासकर Calculus, Vectors जैसे topics।
9. 📊 Graphs & Diagrams Practice करो – Visual topics के लिए helpful हैं।
10. ❓ Doubts तुरंत Clear करो – देर न करो, जो समझ न आए तुरंत पूछो।

❌ Top 10 Common Mistakes in Class 12 Maths

1. ❌ Formulas भूल जाना – बिना revision के direct questions solve करना।
2. ❌ Steps Skip करना – सिर्फ answer लिखना, steps ना दिखाना।
3. ❌ Units & Signs गलत लिखना – radians/degree या +/– का confusion।
4. ❌ Graphs ठीक से न बनाना – inverse trig, application में गलत graphs।
5. ❌ Concept समझे बिना रटना – Calculus जैसे topics में सिर्फ रटना काम नहीं करता।
6. ❌ Calculation Errors – जल्दी में छोटी-छोटी mistakes करना।
7. ❌ Word Problems Avoid करना – LPP, application वाले सवाल skip करना।
8. ❌ Time Management खराब – लंबे सवालों पर ज्यादा समय लगाना।
9. ❌ Previous Year Questions न करना – पुराने पेपर solve नहीं करना।
10. ❌ Revision Last Moment पर करना – पूरे syllabus की timely revision ना करना।

📊 Summary Table – Inverse Trigonometric Functions (Class 12 Math’s)

🔍 Topic	📘 Details
Definition	Inverse of basic trigonometric functions (sin, cos, tan, etc.) with restricted domains to make them one-one.
Principal Value Branch	<ul><li>sin⁻¹x ∈ [–π/2, π/2]</li><li>cos⁻¹x ∈ [0, π]</li><li>tan⁻¹x ∈ (–π/2, π/2)</li></ul>
Important Identities	<ul><li>sin⁻¹x + cos⁻¹x = π/2</li><li>tan⁻¹x + cot⁻¹x = π/2</li><li>2tan⁻¹x = sin⁻¹(2x / (1 + x²))</li></ul>
Conversions	<ul><li>sec⁻¹x = cos⁻¹(1/x)</li><li>cosec⁻¹x = sin⁻¹(1/x)</li><li>tan⁻¹x = sin⁻¹(x / √(1+x²))</li></ul>
Domain & Range	Varies for each inverse function — see principal value branch
Graph Nature	All inverse trig functions are continuous and increasing/decreasing in their domains
Common Questions	<ul><li>Evaluate expressions</li><li>Prove identities</li><li>Simplify using properties</li><li>Use in calculus</li></ul>
Board Exam Weightage	3–4 marks (short to medium length questions)

---

Conclusion

Class 12 Maths Chapter 2 – Inverse Trigonometric Functions plays a vital role in building a strong mathematical foundation, especially for higher-level topics like Calculus. Understanding this chapter is essential not just for scoring well in board exams but also for cracking competitive exams like JEE Main, NDA, and CUET. Many students struggle with the range, domain, and principal values of inverse functions, which are key to solving complex problems accurately. That’s why having well-organized, neat, and concept-focused handwritten notes becomes extremely important.

Our Class 12 Maths handwritten notes PDF offers clear explanations, all essential formulas, identity proofs, graphs, and previous year questions in one place. These notes are created to provide a smart and time-saving way to revise the entire chapter effectively. Whether you are revising one day before the exam or looking for conceptual clarity during regular study, these notes serve as your perfect study companion.

So, if you’re serious about mastering this chapter and securing excellent marks in Math’s, don’t wait! Download the PDF now, go through it regularly, and practice the included questions. These notes are not just information – they are your step towards consistent improvement and exam success.

---

Tags:-
Class 12 Maths Handwritten Notes PDF Download
Chapter 2: Inverse Trigonometric Functions Solutions PDF | Class 12 Maths | Free Download
Class 12 Maths Notes PDF
Inverse Trigonometric Functions Class 12
Class 12 Maths Handwritten Notes
CBSE Class 12 Maths Notes
Free PDF Download Class 12 Maths
Class 12 Chapter 2 Maths Notes
Inverse Trigonometry Notes PDF
Maths Handwritten Notes for Board Exam
Class 12 Maths Important Formulas
CBSE 12th Maths Chapterwise Notes
Class 12 Maths Preparation Tips
Class 12 Maths Revision Notes
Class 12 Maths Short Notes
NCERT Class 12 Maths Notes
Class 12 Maths Formula Sheet PDF