Question

(c)
(e)
(f)
sin 2x + sin 4x + sin 6x=0
tan 0 + tan 20 + tan 30 = 0
sin 2x. tan x + 1 = sin 2x + tan x [H​

Answer 1

Answer:

(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