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# RD Sharma Class 11 Chapter 9 Solutions (Trigonometric Ratios of Multiple And Sub Multiple Angles)

RD Sharma Solutions for Class 11 Maths Chapter 9 ‘Trigonometric Ratios of Multiple and Sub Multiple Angles’ are ready-made solutions available online for the best practices of the students appearing in the central board of secondary examinations. Not only this, but it provides a comprehensive knowledge of the chapter so that you can face all kinds of questions related to the chapter.

In RD Sharma Class 11 Chapter 9 of the trigonometric ratios of multiple and sub-multiple angles, there are 84 questions divided into three exercises. There is an additional exercise 9 VSAQ (very-short-answer-type-questions) specially designed for you to enhance your speed for solving such equations based questions.  In this chapter, you will learn about the formulas illustrating the trigonometric ratios function and its values of ‘x.

RD Sharma solutions are very beneficial for students to understand the concepts of trigonometry related questions. There is always a chance of an 8-12 mark in questions on the final CBSE exam. So these solutions will give the confidence to attempt the questions irrespective of its difficulty level. RD Sharma solutions by Instasolv provide the solved step by step illustrative examples which are very frequently asked in the CBSE examination. You should follow these solutions before attempting your final exam.

## Topics Covered in RD Sharma Class 11 Maths Chapter 9 Trigonometric Ratios of Multiple and Sub Multiple Angles

In trigonometry, we will find the numbers of formulae of Multiple and Sub Multiple Angles.

•  Multiple Angles:  if x is an angle, then 2x, 3x, 4x are the multiple angles of x.
• Sub multiple Angles: if x is any angle, then x/2, x/3, x/4 is the sub multiple angles of x
• Here are some important formulas for trigonometric ratios:

### The important  formulae for trigonometric ratios of submultiple of an angle are as follows :

1. | sin x/2 + cos x/2 | = √(1 + sin x)
2. sin x/2 + cos x/2 =  + √(1 + sin x), if 2nπ – π/4 ≤ x/2 ≤ 2nπ + 3π/4 = – √ (1 + sin x), or
3. | sin x/2 – cos x/2 | = √(1 – sin x)
4. sin x/2 – cos x/2 =  + √(1 – sin x), if 2nπ + π/4 ≤ x/2 ≤ 2nπ + 5π/4 = – √ (1 – sin x), or
5. tan x/2 = ± √(1-cos x) / (1+cos x)
6. A cos x + B sin x < √A2 + B2

These formulas are totally based on the quadrants and signs may be removed or added according to the function.

1. There are some best results given  when X + Y + Z = π are given :
• sin2 X/2 + sin2  Y/2 + sin2  Z/2  = 1 – 2 sin X/2 sin Y/2 sin Z/2
• cos2 X/2 + cos2 Y/2 + cos2 Z/2  = 2 + 2 sin X/2 sin Y/2 sin Z/2
• sin2 X/2 + sin2 Y/2 – sin2 Z/2  = 1 – 2 cos X/2 cos Y/2 sin Z/2
• cos2 X/2 + cos2 Y/2 – cos2 Z/2  = 2 + 2 cos X/2 cos Y/2 sin Z/2
• tan Y/2 tan Z/2 + tan Z/2 tan X/2 + tan X/2 tan Y/2 =1
1. In the Formula for sin x/2, the sin x can also give value as of sin (nπ + (-1) n) x / 2.
2. In the Formula for tan x/2, the tan x can also be the value of tan of nπ +x/2.

## Discussion of Exercises of RD Sharma Solutions for Class 11 Chapter 9

1. In the first exercise 9.1, there are 50 questions, asking you to prove the given equations by applying certain formulas according to the values of trigonometry.

The common questions related to sin, cos, tan x/2 values are asked.

As per the given formula, you should apply the right application of sin, cos, tan, cot:

For example: | sin A/2 + cos A/2 | = √ (1 + sin A)

| sin A/2 – cos A/2 | = √ (1 – sin A)

1.  In 9.2 exercises, there were 11 questions in total. They are a bit lengthy and time-consuming in nature. It is always advised to have a continuous practise of these questions to attempt them in final exams. Every step is important in such questions and with the right application of formula; you can reach to the conclusion.
2. In 9.3 exercises, there are 10 questions following the same pattern of formulas but very important questions. These are marks fetching if you have a good command of them.
3. Exercise 9-VSAQ is specially designed to give additional time to the most recurring questions in various competitive examinations.

## Benefits of RD Sharma Class 11 Maths Solutions for Chapter 9 by Instasolv

Instasolv is always working for the best of their students. This is a free platform for you to prepare for their dreams.  RD Sharma Class 11 Maths Solutions Chapter 9 help you gain quick knowledge about the loopholes in attempting such tough questions. These solutions are made following the current syllabus of CBSE. RD Sharma Class 11 Maths Solutions Chapter 9 gears up your speed to attempt all questions which generally every student doesn’t attempt due to lack of their preparations. So take advantage of these ready solutions and come out with flying colours. Reach your goals with Instasolv!

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