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
- The sum of the first 2 terms has to be expressed as a product.
- 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.
- 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)
- The common factor has to be taken outside
- 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
- 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
- Express the sum of 2 angles in terms of the third using the identity
A + B + C = π
- Now we need to expand the LHS by taking tangents on both sides
- 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
- Sin x + sin y = 2sin (x+y/2) cos (x-y/2)
- Sin x – sin y = 2cos (x+y/2) sin (x-y/2)
- Cos x + cos y = 2cos(x+y/2) cos (x-y/2)
- 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
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