Solutions for Class 11 Maths Chapter 11 by RD Sharma- Free PDF Download
FAQs on Solutions for CBSE Class 11 Maths Chapter 11 - Trigonometric Equations (By RD Sharma)
1. What is the general method for solving trigonometric equations as per the RD Sharma Class 11 solutions?
The general method provided in RD Sharma solutions for Class 11 Maths Chapter 11 involves a systematic approach. First, simplify the given trigonometric equation using identities to express it in terms of a single trigonometric function. Next, reduce it to one of the basic forms, such as sin x = sin α, cos x = cos α, or tan x = tan α. Finally, apply the corresponding general solution formula to find all possible values for the variable, ensuring compliance with the CBSE 2025-26 syllabus.
2. How do RD Sharma solutions handle trigonometric equations involving squared terms like sin²x or tan²x?
RD Sharma solutions demonstrate how to solve equations with squared terms by converting them into simpler forms. The key steps are:
- Use trigonometric identities like sin²x = (1 - cos2x)/2, cos²x = (1 + cos2x)/2, or sec²x = 1 + tan²x.
- These identities help reduce the degree of the equation, transforming it into a linear equation with a multiple angle (e.g., an equation in terms of cos2x).
- Once transformed, the equation can be solved using the standard methods for general solutions.
3. Are the RD Sharma solutions for Chapter 11 sufficient for mastering both Principal and General Solutions for Class 11 exams?
Yes, the solutions for RD Sharma Chapter 11 provide comprehensive coverage for both types of solutions. The exercises clearly distinguish between finding:
- Principal Solutions: These are the solutions that lie within a specific interval, typically [0, 2π). The solutions guide you on how to identify these specific values.
- General Solutions: These represent all possible solutions and are expressed using an integer 'n' (e.g., x = 2nπ ± α for cosine). The book offers extensive practice problems to master the application of these general formulas, which is crucial for exams.
4. What is the most common mistake students make when finding the general solution for equations like cos x = cos y?
A very common mistake is confusing the general solution formulas for different trigonometric functions. For an equation of the form cos x = cos y, the correct general solution is x = 2nπ ± y. Students often incorrectly use the formula for sine, which is x = nπ + (-1)ⁿy. The RD Sharma solutions help prevent this by providing numerous solved examples where the correct formula is explicitly stated and applied, reinforcing the proper method for each function.
5. How do the methods for solving trigonometric equations in RD Sharma differ when dealing with trigonometric inequalities?
While related, the methods differ significantly. Solving a trigonometric equation gives you specific points, whereas solving an inequality gives you a range or interval of values. The process shown in RD Sharma typically involves:
- First, treating the inequality as an equation to find the critical points where the expression equals zero or is undefined.
- Next, using these points to divide the number line (or the interval [0, 2π]) into different regions.
- Finally, testing a value from each region in the original inequality to determine which intervals satisfy the condition.
6. Why is checking for extraneous solutions important when solving trigonometric equations, and how do RD Sharma solutions guide this?
Checking for extraneous solutions is crucial because certain mathematical operations, like squaring both sides of an equation, can introduce solutions that do not satisfy the original equation. For example, when solving an equation with square roots like √(1 – cos x) = sin x, you must ensure that sin x ≥ 0. RD Sharma solutions often highlight the verification step, where the obtained solutions are substituted back into the original equation to confirm their validity and discard any extraneous roots.
7. What special cases of trigonometric equations are covered in the RD Sharma Class 11 solutions for Chapter 11?
Beyond standard problems, RD Sharma solutions for Chapter 11 cover special cases that require logical reasoning rather than just formulas. A key type is solving equations using the concept of boundedness. For instance, an equation like sin x + cos y = 2 can only be solved by recognizing that the maximum value of sin x and cos y is 1. Therefore, the only possible solution is when sin x = 1 and cos y = 1 simultaneously. This requires an understanding of the range of trigonometric functions.
8. How do the initial exercises in RD Sharma Chapter 11 build a foundation for solving complex trigonometric equations?
The initial exercises, such as Exercise 11.1, are designed to build a strong foundation by focusing on the basics. They primarily deal with finding the principal solutions of simple equations like sin θ = 1/2 or tan θ = -1. By mastering the process of identifying values within the 0 to 2π range, students develop the essential skill of relating angles to trigonometric ratios. This fundamental understanding is necessary before moving on to the more abstract concept of general solutions for complex equations in later exercises.
