1.

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

Answer»

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.



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