Question

prove that Sin6x+Sin2x-Sin4x=0​

Answer 1

Step-by-step explanation:

(sin2x+sin6x)−sin4x=0

⇒2sin(

2

2x+6x

)cos(

2

2x−6x

)−sin4x=0

⇒2sin4xcos2x−sin4x=0

⇒sin4x(2cos2x−1)=0

⇒sin4x=0,2cos2x−1=0

⇒sin4x=0,cos2x=

2

1

∴4x=nπ,2x=2nπ±

3

π

∴x=

4

nπ

,nπ±

6

π

where n∈Z

Answer 2

Answer:

let X be 30 degree.

Now we have,

sin 6X = sin 180 = o

sin 4x = sin 120 = sin (180- 60) = sin 60 =(root3) /2

sin 2X = sin 60= (root3)/2

sin 6X + sin2X - sin4X = 0.