Class 11th Math-Unit 10 – Trigonometric Identities

Exercise 10.1

Exercise 10.2

Exercise 10.3

Exercise 10.4

MCQ’s

Unit 10 of the Class 11th Mathematics syllabus focuses on trigonometric identities, which are crucial for simplifying expressions and solving trigonometric equations. Understanding these identities is essential for students as they serve as foundational tools in advanced mathematics and various applications in science and engineering.

Key Topics Covered:

1. Introduction to Trigonometric Identities:
   • Definition: Explanation of what trigonometric identities are and their importance in mathematics.
   • Types of Identities: Overview of the main types of trigonometric identities.
2. Fundamental Trigonometric Identities:
   • Pythagorean Identities: Understanding the relationships derived from the Pythagorean theorem, such as:
     • sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1
     • 1+tan⁡2θ=sec⁡2θ1 + \tan^2 \theta = \sec^2 \theta1+tan2θ=sec2θ
     • 1+cot⁡2θ=csc⁡2θ1 + \cot^2 \theta = \csc^2 \theta1+cot2θ=csc2θ
3. Reciprocal Identities:
   • Reciprocal Relationships: Definitions and formulas for reciprocal identities, such as:
     • sin⁡θ=1csc⁡θ\sin \theta = \frac{1}{\csc \theta}sinθ=cscθ1​
     • cos⁡θ=1sec⁡θ\cos \theta = \frac{1}{\sec \theta}cosθ=secθ1​
     • tan⁡θ=1cot⁡θ\tan \theta = \frac{1}{\cot \theta}tanθ=cotθ1​
4. Quotient Identities:
   • Understanding Ratios: Formulas that express the relationships between the primary trigonometric functions, such as:
     • tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}tanθ=cosθsinθ​
     • cot⁡θ=cos⁡θsin⁡θ\cot \theta = \frac{\cos \theta}{\sin \theta}cotθ=sinθcosθ​
5. Sum and Difference Identities:
   • Sum and Difference Formulas: Formulas for calculating the sine and cosine of the sum and difference of two angles, for example:
     • sin⁡(a±b)=sin⁡acos⁡b±cos⁡asin⁡b\sin(a \pm b) = \sin a \cos b \pm \cos a \sin bsin(a±b)=sinacosb±cosasinb
     • cos⁡(a±b)=cos⁡acos⁡b∓sin⁡asin⁡b\cos(a \pm b) = \cos a \cos b \mp \sin a \sin bcos(a±b)=cosacosb∓sinasinb
6. Double Angle and Half Angle Identities:
   • Formulas: Understanding how to express trigonometric functions of double angles and half angles, which are derived from the sum and difference identities.
7. Applications of Trigonometric Identities:
   • Simplifying Expressions: Techniques for simplifying complex trigonometric expressions using identities.
   • Solving Trigonometric Equations: How to apply identities to solve various trigonometric equations.

Conclusion:

Unit 10 on trigonometric identities equips students with essential tools to manipulate and solve problems involving trigonometric functions. Mastery of these identities is crucial for further studies in mathematics and various applications across different scientific disciplines