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