Q. 4 B5.0( 1 Vote )

# Solve the followi

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.

• cos x = cos y, implies x = 2nπ ± y, where n Z.

• tan x = tan y, implies x = nπ + y, where n Z.

Given,

cos x - cos 2x + cos 3x = 0

To solve the equation we need to change its form so that we can equate the t-ratios individually.

For this we will be applying transformation formulae. While applying the

Transformation formula we need to select the terms wisely which we want

to transform.

As, cos x - cos 2x + cos 3x = 0

we will use cos x and cos 2x for transformation as after transformation it will give cos 2x term which can be taken common.

cos x - cos 2x + cos 3x = 0

-cos 2x + (cos x + cos 3x) = 0

{ cos A + cos B = 2 -cos 2x + 2 cos -cos 2x + 2cos 2x cos x = 0

cos 2x ( -1 + 2 cos x) = 0

cos 2x = 0 or 1 + 2cos x = 0

cos 2x = cos π/2 or cos x = 1/2

cos 2x = cos π/2 or cos x = cos (π/3) = cos (π /3)

If cos x = cos y implies x = 2nπ ± y, where n Z.

From above expression and on comparison with standard equation we have:

y = π/2 or y = π/3

2x = 2nπ ± π/2 or x = 2mπ ± π/3 where m, n ϵ Z

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Solve the followiRD Sharma - Mathematics

3sin2 RD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics

Solve : <span lanRD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics

Solve : <span lanRD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics

Find the general RD Sharma - Mathematics

Find the general RS Aggarwal - Mathematics