To simplify this expression, we first need to remember the trigonometric identities:

sin(A+B) = sinAcosB + cosAsinBcos(A+B) = cosAcosB - sinAsinB

Using these identities, we can rewrite the expression as:

sin(70) + sin(10) / cos(70) - cos(10)
= sin(70)cos(10) + cos(70)sin(10) / cos(70) - cos(10)
= sin(70)cos(10) / cos(70) - cos(10) + cos(70)sin(10) / cos(70) - cos(10)
= (sin(70)cos(10) + cos(70)sin(10)) / (cos(70) - cos(10))

Now, we can use the identity sin(A+B) = sinAcosB + cosAsinB to simplify the numerator:

sin(70)cos(10) + cos(70)sin(10)
= sin(70+10)
= sin(80)

Therefore, the simplified expression is:

sin(80) / (cos(70) - cos(10))