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Trigonometric Functions - II

NIOS · Class 12 · Mathematics

Quick revision notes for Trigonometric Functions - II — NIOS Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

1

Addition and Subtraction Formulae

  • cos(A+B) = cosA cosB - sinA sinB — this is the MASTER formula from which all others are derived
  • cos(A-B) = cosA cosB + sinA sinB — replace B with -B in cos(A+B)
  • sin(A+B) = sinA cosB + cosA sinB — derived using complementary angle identity
2

Product-to-Sum and Sum-to-Product Transformations

  • These formulae convert products of trig functions into sums/differences and vice versa
  • Product-to-Sum: 2sinAcosB = sin(A+B) + sin(A−B)
  • Product-to-Sum: 2cosAsinB = sin(A+B) − sin(A−B)
3

Multiple Angle Formulae (2A and 3A)

  • sin2A = 2sinAcosA = 2tanA/(1+tan²A)
  • cos2A = cos²A − sin²A = 2cos²A − 1 = 1 − 2sin²A = (1−tan²A)/(1+tan²A)
  • tan2A = 2tanA/(1−tan²A)
4

Sub-Multiple Angle Formulae (A/2)

  • A/2, A/3, A/4 are called sub-multiples of A
  • sin(A/2) = ±√((1−cosA)/2) — sign depends on the quadrant of A/2
  • cos(A/2) = ±√((1+cosA)/2) — sign depends on the quadrant of A/2

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Full Notes

Key Concepts

These are fundamental formulae that expressThese formulae convert products of trigonometricThe reverse transformation converts sumsThese formulae express trigonometric functionsThese formulae express trigonometric functions

Frequently Asked Questions

What are the important topics in Trigonometric Functions - II for NIOS Class 12 Mathematics?
Trigonometric Functions - II covers several key topics that are frequently asked in NIOS Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Trigonometric Functions - II — NIOS Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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