To simplify the expression, we first need to use the trigonometric identity:

sin^2 A - sin^2 B = (sinA + sinB)(sinA - sinB)

Therefore, the expression becomes:

((sin1135 + sin35)(sin1135 - sin35))/(sin350*cos370)

Now we can use the following trigonometric identities:

So, sin1135 = sin(1135 - 720) = sin415 = sin(415 - 360) = sin55
Similarly, sin350 = sin(350 - 360) = sin(-10) = -sin10
cos370 = cos(370 - 360) = cos10

Therefore, the expression simplifies to:
((sin55 + sin35)(sin55 - sin35))/(-sin10*cos10)
=> ((sin55 + sin35)(sin55 - sin35))/(-sin20)

Finally, we can use the trigonometric identity:
sin(A + B) = sinAcosB + cosAsinB

So,
sin55 = sin(35 + 20) = sin35cos20 + cos35sin20
sin35 = sin35

Substitute these values back into the expression:
((sin35cos20 + cos35sin20 + sin35)(sin35cos20 + cos35sin20 - sin35))/(-sin20)
= ((sin35 + sin35)(sin35 - sin35))/(-sin20)
= (2sin35*0)/(-sin20)
= 0

Therefore, the final simplified expression is 0.