Official CBSE Assignments for Class 12 Mathematics
Explore structured practice materials through the CBSE Class 12 Mathematics Inverse Trigonometric Functions Assignment Set 05. Tailored for Class 12 learners, utilizing these Mathematics assignments ensures thorough preparation and strengthens foundational knowledge before final CBSE evaluations.
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The domains and ranges (principal value branches) of inverse trigonometric functions are given in the following table:
| Functions | Domain | Range (Principal Value Branches) |
|---|---|---|
| \( y = \sin^{-1}x \) | \( [-1, 1] \) | \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) |
| \( y = \cos^{-1}x \) | \( [-1, 1] \) | \( [0, \pi] \) |
| \( y = \mathrm{cosec}^{-1}x \) | \( \text{R} - [-1, 1] \) | \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\} \) |
| \( y = \sec^{-1}x \) | \( \text{R} - [-1, 1] \) | \( [0, \pi] - \left\{\frac{\pi}{2}\right\} \) |
| \( y = \tan^{-1}x \) | \( \text{R} \) | \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) |
| \( y = \cot^{-1}x \) | \( \text{R} \) | \( [0, \pi] \) |
\( \sin^{-1}x \) should not be condused with \( (\sin x)^{-1} \). In fact \( (\sin x)^{-1} = \frac{1}{\sin x} \) And similarly for other trigonometric functions
- The value of an inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.
For suitable values of domain, we have
- \( y = \sin^{-1} x \Rightarrow x = \sin y \)
- \( x = \sin y \Rightarrow y = \sin^{-1} x \)
- \( \sin(\sin^{-1} x) = x \)
- \( \sin^{-1}(\sin x) = x \)
Key Notes
- \( \sin^{-1}\frac{1}{x} = \mathrm{cosec}^{-1}x \)
- \( \cos^{-1}(-x) = \pi - \cos^{-1}x \)
- \( \cos^{-1}\frac{1}{x} = \sec^{-1}x \)
- \( \cot^{-1}(-x) = \pi - \cot^{-1}x \)
- \( \tan^{-1}\frac{1}{x} = \cot^{-1}x \)
- \( \sec^{-1}(-x) = \pi - \sec^{-1}x \)
- \( \sin^{-1}(-x) = -\sin^{-1}x \)
- \( \tan^{-1}(-x) = -\tan^{-1}x \)
- \( \tan^{-1}x + \cot^{-1}x = \frac{\pi}{2} \)
- \( \mathrm{cosec}^{-1}(-x) = -\mathrm{cosec}^{-1}x \)
- \( \mathrm{cosec}^{-1}x + \sec^{-1}x = \frac{\pi}{2} \)
- \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \)
- \( \tan^{-1}x + \tan^{-1}y = \tan^{-1}\frac{x+y}{1-xy} \)
- \( 2\tan^{-1}x = \tan^{-1}\frac{2x}{1-x^2} \)
- \( \tan^{-1}x - \tan^{-1}y = \tan^{-1}\frac{x-y}{1+xy} \)
- \( 2\tan^{-1}x = \sin^{-1}\frac{2x}{1+x^2} = \cos^{-1}\frac{1-x^2}{1+x^2} \)
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Free study material for Mathematics
Chapter 02 Inverse Trigonometric Functions Printable Assignments & Solutions for Class 12 Mathematics
Download Assignment: Chapter 02 Inverse Trigonometric Functions (Class 12 Mathematics)
Access structured practice assignments for Chapter 02 Inverse Trigonometric Functions designed in alignment with the latest CBSE curriculum for Class 12 Mathematics. These printable sets cover objective and descriptive problem types to support thorough revision.
Why Practice Class 12 Mathematics Assignments?
- Syllabus Compliance: Sets reflect current CBSE evaluation criteria and official marking frameworks.
- Multi-Format Practice: Includes varied problem types designed to deepen comprehension across all sub-topics.
- Time Management: Routine practice optimizes pacing to finish school examinations comfortably within schedule.
Effective Strategy for Class 12 Mathematics Assignments
- Initial Reading: Begin by reading the NCERT book for Class 12 Mathematics to build a baseline understanding.
- Independent Testing: Attempt assignment questions unassisted, then verify work using provided answer keys.
- Supplementary Aids: Leverage revision notes and worksheets whenever you encounter difficult topics.
FAQs
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Yes. These assignments are designed as per the latest CBSE syllabus for 2026. We have included huge variety of question formats such as MCQs, Case-study based questions and important diagram-based problems found in Chapter 02 Inverse Trigonometric Functions.
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