The cos product identity is (where * denotes multiplication and / denotes division)

cos(x)*cos(y) = (cos(x+y) + (cos(x-y))/2

The sin product identity is

sin(x)*sin(y) = (cos(x-y) - (cos(x+y))/2

You cannot simply replace cos with sin.

so for your equation

2*(sin(5x)*sin(2x)) we need to use the sin product identity.

We will first tackle the (sin(5x)*sin(2x)) and after we solve for that, we will substitute it into the original equation

sin(5x)*sin(2x)= (cos(5x-2x)-cos(5x+2x))/2 = (cos(3x)-cos(7x))/2

Plug this back into your equation for (sin(5x)*sin(2x)) and you have 2*((cos(3x)-cos(7x))/2) where the 2s cancel out and you have

= cos(3x)-cos(7x)