Prove that:

sin²(6x) − sin²(4x) = sin(2x) × sin(10x)

∴ L.H.S. = sin²(6x) − sin²(4x)

= (sin(6x) + sin(4x))(sin(6x) − sin(4x))

= [2sin((6x + 4x)/2) × cos((6x − 4x)/2)]  [2cos((6x + 4x)/2) × sin((6x − 4x)/2)]

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

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

= sin(10x) × sin(2x)