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# Best RD Sharma Solutions for Class 11 Maths Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles LIVE
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## RD Sharma Class 11 Solutions for Chapter 9 - Trigonometric Ratios of Multiple and Submultiple Angles (Ex 9.1) Exercise 9.1 - Free PDF

The PDF of solutions for RD Sharma Chapter 9 Trigonometric Ratios of Multiple and Submultiple Angles is provided on Vedantu for the students of class 11 to practice and achieve a good understanding of the concepts. It has been illustratively curated by mathematics experts to help the students of class 11 obtain an in-depth knowledge of trigonometric ratios of multiple and submultiple angles.

Last updated date: 18th Sep 2023
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## Features of RD Sharma Class 11 Maths Chapter 9 Exercise 9.1 Solutions

The free PDF of solutions is easy to download and provides students with an accurate answer to all of the questions in a very simple and understandable language. The answers have been curated by the experts around and according to the needs of the syllabus of the present exams so that students get a good overall score as soon as possible.

The language was kept simple and understandable as it was kept in mind that all the class 11 students should be able to grasp every concept and also to keep the learning process fun and easy for all the students. All the students of class 11 are suggested to refer to this PDF of solutions to score good marks in their exams and gain in-depth knowledge and solutions for a wide range of problems ranging from simple to difficult. The questions on the topic discussed in the PDF, i.e, Trigonometric ratios of multiple and submultiple angles, are one of the most asked in board exams or entrance exams.

The following are some of the most important formulas regarding this topic.

### The Formula for Trigonometric Ratios of Submultiple Angles:

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

• sin A/2 + cos A/2 =  + √(1 + sin A), if 2nπ – π/4 ≤ A/2 ≤ 2nπ + 3π/4 = - √(1 + sin A)

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

• sin A/2 - cos A/2 =  + √(1 - sin A), if 2nπ + π/4 ≤ A/2 ≤ 2nπ + 5π/4 = - √(1 - sin A)

• tan A/2 = ± √(1-cos A) / (1+cos A)

• a cos A + b sin A < √a2 + b2

### The Formula for Trigonometric Ratios of Multiple Angles:

• sin 2A = 2 sin A cos  A

• cos 2A = cos 2 A - sin 2 A

• cos 2A = 2 cos 2 A - 1

• cos 2A = 1 - 2 sin 2 A

• 1 + cos 2A = 2 cos 2 A

• 1 - cos 2A = 2 sin 2 A

• tan 2 A = (1 - cos 2A)/(1+ cos 2A)

• sin 2A = 2 tan A/(1 + tan 2 A)

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

• tan 2A = 2 tan A/(1 - tan 2 A)

• sin 3A = 3 sin A - 4 sin 3 A

• cos 3A = 4 cos 3 A - 3 cos A

• tan 3A = (3 tan A - tan 3 a)/(1 - 3 tan 2 A)

Download this solution PDF for your convenience and start preparing this chapter. Use the conceptual methods of solving the exercise problems given in the textbook and learn how to approach to save time in an exam.

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

1. Will the RD Sharma class 11 solutions for chapter 9 PDF be available offline or is it only viewable online?

The RD Sharma class 11 solutions for chapter 9 free PDF can also be viewed offline once the students complete downloading the PDF. The PDF can be downloaded from here whenever it is necessary for the student. It will also be available online at any time for students to refer to. So, the PDF is always available either online or offline.

2. Is it necessary to study from the RD Sharma class 11 solutions for chapter 9 PDF?

Yes. The PDF is curated by subject matter experts of Vedantu who hold great expertise in mathematics and have put together every single detail that might be necessary for class 11 students for preparing for their board or entrance exams, etc. The topic of Trigonometric ratios of multiple and submultiple angles is an important one and is one of the most basic and beginning things students learn in trigonometry. The formulas of this topic are widely applicable throughout trigonometry. So, it is necessary to prepare this topic well for an overall good score for students.

3. Do students have to solve and learn every single question from the RD Sharma class 11 solutions for chapter 9 PDF?

Yes. Students must learn, practice, and solve every question from the RD Sharma class 11 solutions for chapter 9 PDF as these questions may appear in any kind of exam and it has been made so that the students can have a quick and fun learning session with all the necessary information that can help them score good marks in their exams. This PDF is an academic performance booster for students when it comes to scoring in the board exams, entrance exams, etc. To solve these questions more accurately in exams, students need good practice of these questions to solve them well in the exams eventually.

4. Is it enough to prepare from the RD Sharma class 11 solutions for chapter 9 PDF to perform well in board exams?

Maybe. The RD Sharma class 11 solutions for chapter 9 PDF is a good source of practice for the exams. Students will get to know what all types of questions can be framed and what logical approach they need to put into the problem to solve it. For board exams, this PDF will be enough considering that students also prepare from multiple reference books to score better. It also will in turn be of good help for them in further studies. Increasing conceptual knowledge is mandatory for this subject. It can be done by referring to the solutions and solving exercises of other books.

5. What is the use of studying trigonometric ratios of multiple and submultiple angles?

The trigonometric ratios of multiple and submultiple angles hold good values in the point of view of an exam. It includes basic topics on which trigonometric problems are highly based. It is one of the most important topics of the trigonometry chapter and students study this topic as one of the primary things in trigonometry. While solving trigonometry problems, there can be multiple approaches towards solving a problem, and the more the number of concepts the students study, the more the number of approaches they can perform while solving a problem.