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Solutions for CBSE Class 11 Maths Chapter 11 - Trigonometric Equations (By RD Sharma)

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Last updated date: 12th Apr 2024
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Solutions for Class 11 Maths Chapter 11 by RD Sharma- Free PDF Download

Solutions for Class 11 Mathematics Chapter 11 “Trigonometric Equations” by RD Sharma are available here at Vedantu solved by expert teachers as per the latest CBSE Board syllabus and NCERT Book guidelines. ‘Trigonometric Equations’ is the eleventh chapter in the CBSE Mathematics textbooks for Class 11 students. ‘Trigonometric Equations’ chapter is explained majorly related to Class 11 consists of trigonometric equations concepts. These equations contain unknown angles which are found in trigonometric forms. These values cover the Trigonometric Equations Class 11 syllabus. Students are suggested to use RD Sharma Class 11 Chapter 11 Solutions as the best reference material that helps them to score more marks in their exams. 

Question: How can we download solutions for Class 11 Mathematics Chapter 11 “Trigonometric Equations” by RD Sharma?

Answer: Students can download the solutions Class 11 Mathematics Chapter 11 “Trigonometric Equations”  by RD Sharma from Vedantu.com. 

RD Sharma Class 11 Chapter 11 Solutions are the best material for weak students who feel difficulty in solving trigonometric equations. The chapter-wise examples in RD Sharma make a student boost his confidence before exams. The exercises have a collection of different problems that improve the knowledge of the student. With the help of this, you also get an idea of time management regarding answering the questions in a particular period.

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Class 11 RD Sharma Textbook Solutions Chapter 11 - Trigonometric Equations

What are Trigonometric Equations?

The Trigonometric Equations Class 11 are ones which have trigonometric quantities and ratios of not known angles. The trigonometric ratios can be from the six ratios we have: secant, cosec, cosine, sine, cotangent and tangent. For example, 2 sinx + cos2(2x) + 1 = 0 and sinx = 0. From the above trigonometry equation Class 11, it is obvious that x is the variable, and it is the unknown angle. Hence, suppose for the equation sinx=0, we need to calculate all the values of x for which the expression sinx is equal to zero. Also have a look at Exercise 11.1 to cover all the questions.

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What is The Method to Solve Trigonometry Equations?

Students must pay more attention while solving Trigonometric Equations for Class 11. Each question has a different approach to complete. Let's discuss some basic question patterns and types.

First Type: Some equations can be written in terms of quadratic format, factor multiplication or equations that can get factorized. Here, in the first type, we will discuss such equations. The first step is to convert the equation to factors and then solve each element individually. The final result will be the result of the union of all the solutions that came from each aspect. 

Second Type: For final exams, these types of equations are very important. Such equations can be found in RD Sharma Class 11 Chapter 11 solutions. These equations can be written in the form of x cosA + y sinB = z. The first step is to convert the given equation to the general form of x cosA + y sinB = z. Then secondly you need to assume, x = a cos(theta) and y = a sin(theta). Again let us say, a = √(x2 + y2) and tan(theta) = y/x. After the substitution step we get {a cos(theta)cosA + a sin(theta)sinB = z}. Now one can deduce the answer with cos(A-B) and get the final solutions.

Third Type: Here, we need to study the equations which require transformation from trigonometric function sum form to product form. In such equations, each angle is different with a different value. What one needs to do is put the equation in the sinA + sinB record. Hence from here, you can get each angle familiar on both sides.

Fourth Type: The fourth type of question is also given in RD Sharma Class 11 trigonometric equation solution. It is the reverse process of the previous type. Here the product form of trigonometric functions is transformed to a sum state. The trigonometric ratios of products need to transform into the sum term. Then you can simplify it.

Fifth Type: There are some equations where you need the substitution process or variable change to solve it. You can find ample of such problems in RD Sharma Class 11 trigonometric equation solution series. If an equation involves f( sinA +- cosA, sinAcosA ) = 0 where f(x, y) is one polynomial term, then here we have a special type of substitution process. Here it would help if you substituted sinA +- cosA = z. Then we can again rewrite the same as 1 +- 2 sinAcosA = z2. Therefore, sinAcosA = +- (z2 -1)/2.

RD Sharma Class 11 Chapter 11 Solutions

This chapter provides an overview of trigonometric equations (the equations containing trigonometric functions of unknown angles are known as trigonometric equations). For students who have trouble understanding the concepts of this chapter, Vedantu's experts have designed content based on students' ability to understand them. Students can solve chapter-wise problems by increasing their level of confidence before attending a board exam. Trigonometric Equations comprise one exercise and the RD Sharma Solutions provided on this PDF provide solutions to the questions which are present in the exercise. 

Now, Let's Look at the Topics Mentioned in this Chapter:

  • Definitions.

  • General solutions of trigonometric equations.

  • General solutions of trigonometric equations in specific forms.

Tips on How to Prepare for Exams Using Trigonometric Equations Class 12 RD Sharma

Vedantu gives top-notch content on Trigonometric Equations as per the exam pattern of CBSE by thoroughly checking the weightage of the marks. 

Students can follow the mentioned tips while going through this PDF of RD Sharma Class 11 Chapter 11 Solutions.

  • First, brush up on the basics from previous classes of trigonometric functions.

  • Read the question carefully before answering. When solving RD Sharma questions, we advise students to not look at the solutions directly. Instead, first, solve the solutions on your own and later compare them with RD Sharma Trigonometric Equations Class 11 Solutions. By doing this students will get a proper idea of how to solve a particular problem in Trigonometric Equations. 

  • Since Vedantu provides a step-by-step approach to solutions, students can easily prepare without missing any steps. This helps students to grasp all intermediate steps used while solving the problems.

  • If students want to gain more subject knowledge on the topic and to excel in the examination, they can solve the extra practice and exercise problems that are provided in this free PDF of RD Sharma Trigonometric Equations Class 11 Solutions.

Solved Examples

Q1. What Are the Essential Trigonometric Functions?

Answer: The fundamental trigonometric functions include cosine, sine and tangent functions.

Q2. Write Down the Three Identities of Trigonometry.

Answer: The fundamental trigonometric identities are: sin²a + cos²a = 1, tan²a + 1 = sec²a and cot²a + 1 = cosec²a.

Conclusion

Students will be confident while studying through this PDF of RD Sharma Trigonometric Equations Class 11 Solutions. The solutions to every problem are designed carefully in a step-by-step manner so that students feel that they have covered all their basics on Trigonometric Equations before sitting for their exams. Students can download free PDFs available on the Vedantu platform.

FAQs on Solutions for CBSE Class 11 Maths Chapter 11 - Trigonometric Equations (By RD Sharma)

1. What can other types of questions and solutions be found in RD Sharma Class 11 Solutions Chapter 11?

Another type of equation is where you need to apply the theory of boundedness. Such concepts can be only used for special cases and not for very random cases. Here we need to remember a few points like -1<= sinA <= 1 and -1<= cosA <= 1, tanA belongs to R and cotA belongs to R. Another point is |cosec A| >= 1 and |sec A| >= 1. We have yet another special form that is f(y) = √(z(y)). Here we have two main conditions. The first one f(y) >= 0, z(y) >= 0 and the other one is f2(y) = z(y). Let's take an example √(1 – cosB) = sinB. All such questions can be found in RD Sharma Class 11 solutions Chapter 11 portion.


2. What do you mean by trigonometric inequalities in Maths Class 11 Trigonometric Equations?

An inequality that has trigonometric functions of an unknown angle value is called trigonometric inequality. Basic trigonometric equations have a specific form. Trigonometric inequalities are very similar to linear inequalities. The major difference between the two is that trigonometric inequalities have trigonometric ratios in place of general variables.


Generally such equations are of the form P( f(a), g(a)….) < (or >) 0, where f(a) or g(a) are normal trigonometric functions. 'Vedantu' provides free study materials which can be downloaded from the Vedantu site and app.

3. How can Vedantu's RD Sharma Class 11 Chapter 11 Solutions cover all the formulae?

This solution pdf can cover many related formulae like The fundamental trigonometric identities etc at once. Along with those, it will also explain how the application solves the trigonometric equations with examples. This provides many examples with simple answers. Vedantu’s RD Sharma Solution helps you cover all the problems of trigonometric equations including using trigonometric functions. Vedantu also provides other free materials like the latest syllabus, sample papers, question banks, and solutions to old question papers.

4. Do Vedantu’s RD Sharma Solutions follow the newly updated Mathematics syllabus?

Yes, Vedantu’s RD Sharma solutions for Class 11 Mathematics Chapter 11 “Trigonometric Equations” are prepared as per the latest CBSE Board syllabus and NCERT Book guidelines. This RD Sharma solutions pdf solution material is specially prepared by subject matter experts in India and is highly recommended to students of Class 11th CBSE. These solutions are provided free of cost and there are no additional charges. In addition to the free solutions, Vedantu also provides free online classes for Maths subject undertaken by professional teachers in the field of Mathematics. 


5. What is the main advantage of having RD Sharma solutions for CBSE Class 11 Mathematics solutions for Chapter 11?

Having a pdf that has RD Sharma's solutions of CBSE Class 11 Mathematics Chapter 11  is a great resource to practice what we learned in Chapter 11. There are many advantages of having RD Sharma's solutions of CBSE Class 11 Mathematics Chapter 11 PDF. By working on this chapter with the help of this solution PDF, students can also improve their time management skills.  With the help of RD Sharma's solutions PDF, students will be able to understand the important formulas in a simple way.  Hence, students can score well by enhancing all these.