RD Sharma Class 11 Chapter 7 Solutions (Trigonometric Ratios of Compound Angles)

RD Sharma Class 11 Maths Solutions Chapter 7 Trigonometric Ratios of Compound Angles is here to help you to understand the chapter. In RD Sharma Solutions for Class 11 Chapter 7, we will learn the value of a Trigonometric Function at the sum or difference, the maximum and minimum value of Trigonometric expression, various types of angles, their properties and few theorems.

This chapter consists of 4 exercises and around 90 questions. We have solved all 90 Questions below. In the first exercise, you will be asked to evaluate the value of trigonometric functions at sum or difference and in a few questions, we will prove the theorems. In the second exercise, you will solve the problems of maximum and minimum value of trigonometric expressions and the expression of certain algorithms. 

InstaSolv has taken measures to support you inhibit the knowledge of every concept with our combination of expertise and clear vision. A trigonometric ratio is something which gives you a great opportunity to score in your examinations. With our solutions, you will find the easier way to solve the theorems and expressions. Evaluating values is made simple for you with our step by step formula. A detailed explanation of all Trigonometric Functions included in our solutions.

Topics covered in RD Sharma solutions for Class 11 Chapter 7

Trigonometry and Compound Angle

Trigonometry, A study of angles, uses its three basic functions of sine, cosine and tangent to derive its calculations. An angle which is made up of the algebraic sum of two or more than two angles is termed as a compound angle. In simple language, when any angle is added or subtracted, the result we see is called Compound Angle.

Formulas for compound Angle

We use the formula of compound Angle to find the sum and difference of functions in Trigonometry. It deals with functions like (A+B) and (A-B). We here have 6 basic formulas of each function.

The  sum and differences formulas of sine, cosine and tangent are; 

  • sin (X + Y) = sin X cos Y + cos X sin Y
  • cos (X + Y) = cosX cosY – sinX cosY
  • tan (X + Y) = [tanX + tanY] / [1 – tanX tanY]
  • sin(X – Y) = sinA cosY – cosX sinY
  • cos(X – Y) = cosX cosY + sinX sinY
  • tan(X – Y) = tanX – tanY/ 1 + tan X tanY

Multiples Angle

When the identities are involved with numbers, it is called multiple angle identities. For instance, Sin 2X, Cos 2Y, Tan 2X, Sin 3X.

Thus, here we denote further various formulas for multiple angles. 

  • Sin2X= 2SinX CosX= 2Tan X/1 + Tan 2X
  • Cos2X= Cos2X – Sin 2X = 1- 2Sin2X= 2Cos2X-1= 1-Tan2 X/1 + Tan2X
  • Tan 2X = 2TanX/1- Tan2X

Transformational Formula

Here, we have two sets of transformational Formula

  1. Sum or difference of identities into Product:
  • 2sinXcosY = sin (X + Y) + sin (X – Y)
  • 2cosXsinY = sin (X + Y) – sin (X – Y)
  • 2cosXcosY = cos (X + Y) + cos (X – Y)
  • 2sinXsinY = cos (X – Y) – cos (X + Y)
  1. Product into sum or difference of identities:
  • sin X + sinY = 2sinX + Y/2 cos X – Y/2
  • cos X + cosY = 2cos X – Y/2 cos X + Y/2
  • tan X + tanY = sin (X + Y)/ cos X. cos Y

Exercise-Discussion of RD Sharma Class 11 Chapter 7

  1. This chapter runs on formulas. With the practice of both the exercises, you can achieve the ability to solve various trigonometric problems.
  2. Application of the right formula is necessary to score here. With the help of RD Sharma Class 11 Maths Solutions Chapter 7, you can avail the understanding of the logical method of formulation. 
  3. Perhaps you may find Multiple Angle a bit difficult but with the understanding of formulas, you can get the better refinement of the concept.
  4. Both the exercises give you a thorough trigonometric knowledge including the concept of compound angle, multiple angles, inverse function and their properties. 
  5. The transformational formula is used to transform products into sum or difference of functions or vice versa.
  6. A short and simple technique is used to identify the expression of Angles.
  7. The solution has a proper diagram representation to understand the compound angles.

Benefits of RD Sharma Class 11 Chapter 7 Solution by InstaSolv

  1. InstaSolv has gathered all the solutions accordingly with the simplest method.
  2. When the chapter is based on a formula, it becomes tough to remember it, we have described the formulations in such a way that you will instantly memorize it.
  3. InstaSolv covers all types of basic and advanced level questions to provide the whole understanding of the chapter.
  4. Learning Trigonometry will help you in future whether you go in the field of designing, medical or business. 
  5. Trigonometry enhances your problem-solving skills and makes you adaptable for unseen circumstances.