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

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.