Question

Prove that sin 4A = 4 sin A × cos 3 A - 4 cos A × sin 3 A

Answer 1

R.H.S:
4sinAcos³A-cosAsin³A
=4sinAcosA(cos²A-sin²A)
=2.2sinAcosA(cos2A) [cos²A-sin²A=cos2A and 2sinAcosA=sin2A]
=2sin2Acos2A
=sin(2.2A)
=sin4A=L.H.S(Proved)