Unit 5 - Trigonometry | Solution of Trigonometric Equations

Solution of Trigonometric Equations is the fifth chapter in Trigonometry for Class 10 students who are studying Optional Mathematics subject.

This is the chapter requiring complete implication of the rules and formulae we discussed in the first three chapters: multiple angles, sub-multiple angles and transformation of triogonometric ratios.

Related Solutions:

Exercise 2


1. Solve the following trigonometric equations: ($0^o \leq \theta \leq 180^o$)

a) $cos \theta = cos ( \pi - 2 \theta)$

Solution:

$cos \theta = cos ( \pi - 2\theta)$

$or, \theta = 180^o - 2\theta$

$or, 3 \theta = 180^o$

$\therefore \theta = 60^o$


b) $sin 2 \theta = sin \left ( \dfrac{\pi}{2} - \theta \right)$

Solution:

$sin 2 \theta = sin \left ( \dfrac{\pi}{2} - \theta \right)$

$or, 2 \thtea = \dfrac{ \pi}{2} - \theta$

$or, 3 \theta = 90^o$

$\therefore \theta = 30^o$


c)

Solution:

$tan \left ( \dfrac{3 \pi}{2} - \theta \right) = tan \theta$

$or, \dfrac{3 * 180}{2} = 2 \theta$

$or, \theta = \dfrac{3*90}{2}$

$\therefore \theta = 135^o$


2. Solve the following trigonometric equations: ($0^o \leq A \leq 180^o$)

a)

Solution:

$sinA - tan A = 0$

$or, sin A = tan A$

$or, sin A = \dfrac{sinA}{cosA}$

$or, cos A = 1$

$\therefore A = 0^o or 180^o$


b)

Solution:

$2sinA = tanA$

$or, 2 sin A = \dfrac{sinA}{cosA}$

$or, cosA = \dfrac{1}{2}$

$\therefore A = 60^o$

Also,

=

c)

Solution:

$4cosA = 3secA$

$or, 4 cosA = 3 * \dfrac{1}{cosA}$

$or, cos^2 A = \dfrac{3}{4}$

$or, cos A = \pm \sqrt { \dfrac{3}{4}}$

$or, cosA = \pm \dfrac{ \sqrt{3}}{2}$

Taking positive sign,

$cos A = \sqrt{3}{2}$

$\therefore A = 30^o$

Taking negative sign,

$cosA = - \sqrt{3}{2}$

$\therefore A = 150^o$


d) 

Solution:

$2cosA = cotA$

$or, 2 cos A = \dfrac{cosA}{sinA}$

$or, sinA = \dfrac{1}{2}$

$\therefore A = 30^o$

Also, $A = (180 - 30) = 150^o$

Again,

Values of cos and cot are identical at $A = 90^o$.

Thus, the required values of A are $30^o, 90^o, 150^o$.



About Readmore Optional Mathematics Book 10

Author: D. R. Simkhada
Editor: I. R. Simkhada

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Class 10 - Solution of Trigonometric Equations - Trigonometry Solved Exercises | Readmore Optional Mathematics is a collection of the solutions related to solution of trigonometric equations of Trigonometry for Nepal's Secondary Education Examination (SEE) appearing students.

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