Prove the following identities:
sin 4x = 4 sin x cos3 x – 4 cos x sin3 x
To prove: sin 4x = 4 sin x cos3 x – 4 cos x sin3 x
Proof:
Take LHS:
sin 4x
Identities used:
sin 2x = 2 sin x cos x
cos 2x = cos2 x – sin2 x
Therefore,
= 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 x cos x
= RHS
Hence Proved