Question -
Answer -
Let us consider LHS:
sin 4x
We know, sin 2x = 2 sin x cos x
cos 2x = cos2 x – sin2 x
So,
sin 4x = 2 sin 2x cos 2x
= 2 (2 sin x cos x) (cos2 x – sin2 x)
= 4 sin x cos x (cos2 x – sin2 x)
= 4 sin x cos3 x – 4 sin3 xcos x
= RHS
Hence proved.