Prove that sin<su

To Prove: sin² 6x – sin² 4x = sin 2x sin 10x
Proof:

RHS = sin 2x sin 10x

LHS = sin² 6x – sin²4x

we know that,

 [a² – b² = (a – b)(a + b)]

LHS = (sin 6x – sin 4x) (sin 6x + sin 4x)

Rearranging we get

LHS = (2 × sin x × cos x)(2 × sin 5x × cos 5x)

LHS = sin 2x sin 10x [∵ 2sin A cos A = sin 2A]

∴ LHS = RHS

Hence, proved