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# RD Sharma Class 11 Solutions Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Last updated date: 26th Nov 2023
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## Download Important RD Sharma Solutions for Class 11 Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Exercise 9.3 Free PDF

You can download a free PDF of RD Sharma Class 11 Solutions for Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Exercise 9.3, solved by subject-matter experts of Vedantu. You can avail these PDFs for free both from the website of Vedantu and its mobile application. All the questions of Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Exercise 9.3 come with solutions. The RD Sharma Class 11 Maths helps you to revise the complete syllabus and score more marks in the exams. You can also register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams on Vedantu.

## Introduction of RD Sharma Class 11 Solutions for Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Exercise 9.3

Exercise 9.3 discusses problems based on the values ​​of trigonometric functions of ‘x’ according to the values ​​of ‘x / 3’. The solutions here are explained in simple and understandable language that helps the students to develop their problem solving and analytical skills. The presentation of each solution to this task is explained uniquely by the expert teachers at Vedantu. To get good marks, practising RD Sharma Class 11 Maths Solutions can be very helpful. A PDF of RD Sharma Solutions Mathematics Class 11 Chapter 9 Exercise 9.3 is provided here, which students can download for free easily.

RD Sharma Solutions are organized by expert teachers based on the current CBSE board syllabus to help students succeed in their board exams. Now let's look at the concepts discussed in this chapter.

• Values ​​of trigonometric functions in ‘2x’ in terms of ‘x’ values.

• Values ​​of trigonometric functions in ‘x’ in terms of values ​​in ‘x / 2’.

• Values ​​of trigonometric functions in ‘x / 2’ in terms of ‘cos x’ values.

• Values ​​of trigonometric functions in ‘3x’ depending on the values ​​in ‘x’.

• Values ​​of trigonometric functions in ‘x’ in terms of values ​​in ‘x / 3’.

• The values ​​of trigonometric activity in some points are important.

### What does the RD Sharma Class 11 Solutions for Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles Exercise 9.3 Consist of?

The RD Sharma Class 11 Solutions Chapter 9 Exercise 9.3 consists of various sums related to trigonometric ratios of multiple and submultiple angles. The 9.3 exercises consist of 10 questions following the same pattern of formulas and are very important for the students to get good marks in the exams. These are marks fetched if you have a good command of them and if you study consistently putting diligent efforts.

The solutions for exercise 9 are specially designed to give additional time to the most recurring questions in various competitive examinations.

## FAQs on RD Sharma Class 11 Solutions Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles

1. What are the benefits of using RD Sharma Class 11 Solutions Chapter 9 by Vedantu?

Vedantu always works for the welfare of their students. This is a forum with free and easy to access material that helps prepare the students to achieve their dreams. RD Sharma Class 11 Solutions Chapter 9 helps you get quick information about opportunities to try such difficult questions. These solutions are implemented following the current CBSE syllabus. RD Sharma Class 11 Solutions Chapter 9 Trigonometric Ratios on Multiples and submultiple adjusts your pace so you can try all the questions that every student should achieve good marks in the final exams.

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3. What do the RD Sharma Class 11 Solutions Chapter 9 Trigonometric Ratios on Multiples and submultiple cover for the Class 11 finals?

The smart solutions for the Class 11 Chapter 5 RD Sharma chapter that Vedantu brings to class 11 students include:

• Answers to all questions, numbers and problems included in the RD Sharma Class 11 Chapter 9 Trigonometric Multiple and Submultiple Angles Maths Textbook.

• A detailed diagram to answer all problems (in more than one way if possible).

• A description of all the chapters and formulas used to summarize the question.

• Use algorithmic methods to achieve a solution to any given question.

4. What are the key features of RD Sharma Class 11 Solutions Chapter 9 Trigonometric Ratios on Multiples and submultiple?

The Features of RD Sharma Maths Solutions for Class 11 Chapter 9 Trigonometric Multiples and Submultiples are as follows:

• The RD Sharma Class 11 Solutions Chapter 9 Trigonometric Ratios on Multiples and submultiple are developed by our subject specialists

• The RD Sharma Solutions are easily accessible online

• The solutions are made according to the latest CBSE syllabus pattern

• The RD Sharma Solutions are Smart solutions based on analytical skills and concept building.

• A simple preparation tool

5. What are compound and submultiple angles?

Compound Angles - Angles made up of a total algebraic sum or difference of two or more angles are called compound angles. Trigonometric ratios of compound angles include an examination of the trigonometric value of the trigonometric difference of two or more angles. Some of the trigonometric identities regarding compound angles are listed below:

• Sin (A + B) = sinA cosB + cosA sinB

• Sin (A - B) = sinA cosB - cos A sin B

• Cos (A + B) = cosA cosB - sinA sinB

Submultiple Angles - As the name suggests, the trigonometric ratio of a submultiple of an angle means when we try to determine the trigonometric value of an A / 2 or A / 3 angle.

Other Trigonometric Features of the Submultiple Angle are:

• | Sin A / 2 + cos A / 2 | = √ (1 + sin A)

• | Sin A / 2 - cos A / 2 | = √ (1 - sin A)

• tan A / 2 = ± √ (1 - cos A) / (1 + cos A)