Question

सिद्ध कीजिए: $\sin x + \sin 3x + \sin 5x + \sin 7x = 4 \cos x\,\cos 2x\,\sin 4x$

Answer 1

Step-by-steptep-by-step explanation:

L.H.S

sin x+ sin 3x+ sin 5x + sin 7x= (sin 7x+ sin x)+ (sin 5x + sin 3x)

= 2 sin(7x+x)/2 cos (7x-x)/2 + 2 sin(5x+3x)/2 cos(5x-3x)/2

= 2 sin 4x cos 3x+ 2 sin 4x cos x

= 2 sin 4x( cos 3x+ cos x)

= 2 sin 4x( 2 cos3x+x/2 cos 3x-x/2)

= 2 sin 4x( 2 cos 2x cos x)

= 4 cos x cos 2x sin 4x

= R.H.S