Question

find the general solution of sin2x-4sin4x+sin 6x=0​

Answer 1

Answer:

sin2x−sin4x+sin6x=0

as we know that, (sin a+ sin b=2sin(a+b2)cos(a−b2))

so, 2sin4x.cos(−2x)−sin4x=0

=sin4x(2cos2x−1)=0

now it can possible that whether sin4x=0or2cos2x−1=0

when sin4x=0

4x=nπ& n ∈z

x=nπ4

when 2cos2x−1=0

cos2x=cos(π3)

2x=2nπ±π3

x=nπ±π6

answer = nπ4,nπ±π6

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