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RS Aggarwal Class 11 Chapter 16 Solutions (Conditional Identities Involving The Angles of A Triangle)

RS Aggarwal Class 11 Solutions for Chapter 16 are a basic study guide for you to excel in this chapter. This chapter begins with some trigonometric formulae of Sin and Cos and further teaches you how to find the angles of a triangle using trigonometric identities. The chapter consists of 1 exercise which has 12 questions in it.

Chapter 16 of RS Aggarwal Class 11 Book is relatively simple but involves the usage of different trigonometric identities. So, you might find it tricky at first. But, with the best RS Aggarwal solutions with you, revising these formulae and identities is easy.  We have provided clear explanations for all the 12 questions so that you can answer any questions related to these in the CBSE exams.

Important Topics for RS Aggarwal Class 11 Solutions for Chapter 16 – Conditional Identities Involving the Angles of a Triangle

Type 1 Identities Involving Sines and Cosines

Method

  1. The sum of the first 2 terms has to be expressed as a product.
  2. Express the sum of 2 angles made in terms of the third angle, using the formula A + B + C = π, in the product which is received.
  3. Now we need to expand the 3rd term by using any of the following relations mentioned below:
  • Sin 2θ = 2sinθ cosθ
  • Cos 2θ = (2cos²θ – 1) = (1 – 2sin²θ)
  1. The common factor has to be taken outside
  2. The trigonometric ratio of a single angle is to be expressed into a sum of 2 angles by using the necessary formula.

Type 2 Identities Involving Square of Sines and Cosines

Method

  • The square of sines and cosines needs to be changed into cosines of double of the angles using the formula mentioned below:
  • Cos²θ = ½(1 + cos2θ)
  • Sin²θ = ½(1 – cos2θ)

Type 3 Identities Involving Tangents

Method

  • Express the sum of 2 angles in terms of the third using the identity

A + B + C = π

  1. Now we need to expand the LHS by taking tangents on both sides
  2. The final step is to cross multiply and transpose

The same method has to be followed for identities involving contingents

Important Formulas to be Used in the Chapter

  1. Sin x + sin y = 2sin (x+y/2) cos (x-y/2)
  2. Sin x – sin y = 2cos (x+y/2) sin (x-y/2)
  3. Cos x + cos y = 2cos(x+y/2) cos (x-y/2)
  4. Cos x – cos y = -2sin (x+y/2) sin(x-y/2)

Exercise Discussion of RS Aggarwal Class 11 Chapter 16  – Conditional Identities Involving the Angles of a Triangle

This exercise 16 has 12 questions in which you have to:

  • Prove the trigonometric equation when angles of a triangle are given
  • Prove the trigonometric equation when angles of a triangle are given using the formulas
  • Prove the trigonometric equations using identities

Benefits of RS Aggarwal Class 11 Solutions for Chapter 16 – Conditional Identities Involving the Angles of a Triangle

Instasolv is one of the best platforms for students to learn maths. RS Aggarwal Solutions for Chapter 16 – Conditional Identities Involving the Angles of a Triangle, prepared by our best subject matter experts are easy to use and understand. You can further ask us any query related to the chapter or any other concept related to CBSE Class 11 Maths Syllabus and we will provide you instant solutions. We ensure 100% error-free RS Aggarwal Solutions for Class 11 students.