HSC Arts 12th Board ExamMaharashtra State Board
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# Find the general solution of the equation sin 2x + sin 4x + sin 6x = 0 - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptTrigonometric Functions General Solution of Trigonometric Equation of the Type

#### Question

Find the general solution of the equation sin 2x + sin 4x + sin 6x = 0

#### Solution

(sin 2x +sin 6x)+sin 4x =0

2sin4x.cos2x+sin4x=0

sin4x(2cos2x+1)=0

sin 4x=0 or 2cos2x+1=0

sin4x=0 or cos2x=-1/2=-cospi/3=cos(pi-pi/3)

Using sinx=0=>x=npi

sin4x=0

4x=npi

The genral solution is x

x=(npi)/4

using cosx=cosalpha=>x=2mx+-alpha

cos2x=cos((2pi)/3)

2x=2mpi+-(2pi)/3

The genral solution is x

x=mpi+-pi/3 where m,n in z

Is there an error in this question or solution?

#### APPEARS IN

2016-2017 (March) (with solutions)
Question 2.1.3 | 3.00 marks
2016-2017 (July) (with solutions)
Question 3.1.2 | 3.00 marks
Solution Find the general solution of the equation sin 2x + sin 4x + sin 6x = 0 Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type.
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