Answer :

Given,


sin x – 3sin2x + sin3x = cos x – 3cos2x + cos3x


To solve the problem we need to apply transformation formula, but we need to group sin x and sin 3x together and similarly cos x and cos 3x in RHS side.


sin x + sin3x – 3sin2x = cos x + cos3x – 3cos2x


Transformation formula:


cos A + cos B =


sin A + sin B =



2sin 2x cos x – 3sin 2x = 2cos 2x cos x – 3cos 2x


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


2cos x (sin 2x – cos 2x) -3(sin 2x – cos 2x) = 0


(sin 2x – cos 2x)(2cos x – 3) = 0


cos x = 3/2 or sin 2x = cos 2x


As cos x [-1,1]


no value of x exists for which cos x = 3/2


sin 2x = cos 2x


tan 2x = 1 = tan π/4


We know solution of tan x = tan α is given by –


x= nπ + α , n Z


2x = nπ + (π/4)



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
caricature
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 RD Sharma - Mathematics