If sin4x+sin2x=0 then find the principal solution.

 Steps to solve If sin4x+sin2x=0 then find the principal solution.

⇒sin4x+sin2x=0

⇒2sin(4x+2x)/2.cos(4x-2x)/2=0

⇒2sin3x.cosx=0

⇒sin3x=0, cosx=0

⇒3x=nπ, x=(2n+1)π/2

⇒x=nπ/3

n=0, x=0

n=1, x=π/3

n=2, x=2π/3

n=3, x=π

n=4, x=4π/3

n=5, x=5π/3

Hence the principal solution of sin4x+sin2x=0 are 0, π/3, 2π/3, π, 4π/3, 5π/3

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