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Formula Sheet

Inverse Trigonometric Functions — Formula Sheet

Madhya Pradesh Board · Class 12 · Mathematics

6 formulas from Inverse Trigonometric Functions (Madhya Pradesh Board Class 12 Mathematics) on one page, grouped by topic.

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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6 Entries · 3 Sections

Formulas and Key Relations

1. Core idea and principal values

sin(sin^-1 x) = x, x ∈ [-1, 1] and sin^-1(sin x) = x, x ∈ [-π/2, π/2]

(f^-1 ∘ f)(x) = f^-1(f(x)) = f^-1(y) = x

(f ∘ f^-1)(y) = f(f^-1(y)) = f(x) = y

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.

Key relations

The compositions satisfy (f⁻¹ ∘ f)(x) = x and (f ∘ f⁻¹)(y) = y.

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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 many formulas are in Inverse Trigonometric Functions?
This sheet lists 6 formulas from Inverse Trigonometric Functions, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
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.

More resources for Inverse Trigonometric Functions

All Madhya Pradesh Board Class 12 Mathematics Formula Sheet

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