S.L. Loney Elimination Solutions (Chapter 20)

SL Loney Plane Trigonometry Solutions for Chapter 20 ‘Elimination’ will help you understand the exercise questions of this chapter thoroughly. As the name suggests, Elimination explains how to eliminate variables that are linked to one or more equations. This chapter majorly concentrates on eliminating the angle, ϴ and is one of the easiest chapters in trigonometry that can help you to score good marks in competitive exams. SL Loney Plane Trigonometry Elimination Solutions for JEE are provided in easy to understand language and with complete explanations.

SL Loney Plane Trigonometry Solutions are considered to be a primary source of study material for competitive exams like NEET and IIT JEE. These solutions would shape your concepts from the base level and would help you in practising all the exercises easily. SL Loney Plane Trigonometry Solutions for Elimination include one exercise with 17 questions. All the questions are based on the elimination of the angle from the given equations.

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Important topics for SL Loney Plane Trigonometry Solutions Chapter 20: Elimination

This section covers a few important topics of the chapter like what does elimination mean, define eliminant, how to eliminate variable, and how to eliminate ϴ from the equation and their brief introduction or definition.

  • Elimination: When two equations have one common unknown variable and constants in it then, the common unknown variable states that there is a relation between those 2 equations. The process of adding or subtracting those two-equations to eliminate the common unknown variable from the equation is called Elimination.

For Example:  a x + b = 0; c x2 + d x + e = 0


x = (- b/a)

Hence the second equation become,

c (-b/a) 2 + d (-b/a) + e = 0


c (b/ a) 2 – (d b/a) + e = 0,

b2 c – d b a + e a2  = 0

So, we have eliminated the unknown variable “x” from the second equation.

  • Eliminant: The equation from which the common unknown variable is eliminated is called Eliminant. In the above example, the equation ‘b2 c – d b a + e a2 = 0’ is called eliminant.
  • Eliminating ϴ from the Equation: It means that the equations are combined in a particular manner and a new equation is formed that is valid and doesn’t have ϴ.

For example:  x = a cos ϴ; y = a sin ϴ

Here ‘a’ is a constant parameter, ϴ is the common unknown variable, and x and y equation share a relation if we eliminate ϴ. By squaring both the equation we get:

x2 = a2 cos2 ϴ; y2 = a2 sin2 ϴ

By adding both the equation we get

x2 + y2 = a2 cos2 ϴ + a2 sin2 ϴ = a2 (cos2 ϴ   + sin2 ϴ)

(cos2 ϴ   + sin2 ϴ) = 1;

Therefore, we get

x2 + y2 = a2

The above equation is a new equation which is valid, shows the relation between x and y, and ϴ is eliminated.

Exercise Discussion for SL Loney Plane Trigonometry Solutions Chapter 20: Elimination

  • SL Loney Plane Solutions Trigonometry Elimination has a total of 17 exercise questions in total. Method of how to eliminate ϴ is shown in a few solved examples in this chapter. 
  • The exercise problems are majorly dependent on the topic of how to eliminate ϴ.
  • There are also a few problems that are related to the topic of how to eliminate ɸ. 
  • The questions asked are based on the topic like prove the equations are equal after elimination of ϴ, elimination of (ϴ + ɸ) from the equation, and elimination of ϴ and ɸ from the equations.

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