Question

Prove :
sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x cos 4x

Answer 1

sinx+sin3x+sin5x+sin7x

sinx+7x+sin3x+sin5x

[sin(A+B)]sinC+sinD=2sin

2

C+D

cos

2

C−D

Now,

2sin(

2

x+7x

)cos(

2

x−7x

)+2sin(

2

3x+5x

)cos(

2

3x−5x

)

2sin4xcos3x+2sin4xcosx

2sin4x(cos3x+cosx)

2sin4x[2cos

2

C+D

cos

2

C−D

]

2sin4x[2cos

2

3x+x

cos

2

3x−x

]

2sin4x×2cos2xcosx

4sin4xcos2xcosx.

Answer 2

Answer:

=(sin7x+sinx) +sin4x =sin(4x+ 3x) +sin(4x-3x) +sin4x

= so by using: sin(A+B) + sin(A-B) =2sins. cosB

= 2sin4x.cos3x+sin4x

Step-by-step explanation:

hope its helpful