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Inverse Trigonometric Functions — Syllabus

Madhya Pradesh Board · Class 12 · Mathematics

What Inverse Trigonometric Functions covers in Madhya Pradesh Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

105 questions44 flashcards6 formulas & key relations5 concepts

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A flowchart illustrating the conditions (one-one and onto) required for a function to have an inverse, and what happens if these conditions are not met.
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4 Topics · Madhya Pradesh Board Class 12 Mathematics · 2026-27

Topics in Inverse Trigonometric Functions

1

1. Basic ideas and principal value branches

  • A function has an inverse only when it is one-one and onto.
  • Sine, cosine, secant, cosecant, tangent, and cotangent are not one-one over their natural domains.
  • By restricting the domain, inverse trigonometric functions are defined.
2

2. Domains and principal value ranges

  • sin is one-one on [-π/2, π/2] and has range [-1, 1].
  • cos is one-one on [0, π] and has range [-1, 1].
  • cosec is one-one on [-π/2, π/2] - {0} and has range R - (-1, 1).
3

3. Standard principal values and worked examples

  • The principal value of sin⁻¹(1/√2) is π/4.
  • The principal value of cot⁻¹(-1/√3) is 2π/3.
  • For sin⁻¹(sin x), the answer must be reduced to the principal branch if needed.
4

4. Important identities and simplification patterns

  • Inverse trigonometric expressions are often simplified by substitution.
  • Trigonometric double-angle and triple-angle ideas are useful in inverse problems.
  • Some expressions become simple after using half-angle identities.

Key Concepts

Central concept: Inverse trigonometric functions are defined by restricting trigonometric functions to principal value branches so that the functions become one-one and onto, allowing inverse functions to exist and be used correctly within their domains.

Inverse function ideaPrincipal value branchsin inversecos inversecosec inversesec inversetan inversecot inverse

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Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Inverse Trigonometric Functions include Basic ideas and principal value branches, Domains and principal value ranges, Standard principal values and worked examples, Important identities and simplification patterns. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Inverse Trigonometric Functions for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 105 practice questions on Inverse Trigonometric Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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