To show that sin(2x)cos(3x) = sin(4x)cos(5x), we can use the trigonometric identity:

sin(A)cos(B) = (1/2)*[sin(A+B) + sin(A-B)]

Applying this identity to both sides, we have:

sin(2x)cos(3x) = (1/2)[sin(2x+3x) + sin(2x-3x)]
= (1/2)[sin(5x) + sin(-x)]
= (1/2)[sin(5x) - sin(x)]

Similarly,

sin(4x)cos(5x) = (1/2)[sin(4x+5x) + sin(4x-5x)]
= (1/2)[sin(9x) + sin(-x)]
= (1/2)[sin(9x) - sin(x)]

Therefore, sin(2x)cos(3x) = sin(4x)cos(5x) is not true in general, as they are not equal.