Using the sum-to-product identities, we can simplify the expression as follows:
(sin20sin40sin110)/(sin60sin30+sin20sin40cos110)= (sin20sin40sin110)/((1/2)(2sin60cos30) + sin20sin400)= (sin20sin40sin110)/(sin60cos30)= sin20sin40sin110/sin60cos30= sin20sin40sin110/sin60(2sin30cos30)= sin20sin40sin110/(sin60sin60)= sin20sin40sin110/(3/4)= 4/3 sin20sin40sin110
Therefore, the final simplified expression is 4/3 sin20sin40*sin110.
Using the sum-to-product identities, we can simplify the expression as follows:
(sin20sin40sin110)/(sin60sin30+sin20sin40cos110)
= (sin20sin40sin110)/((1/2)(2sin60cos30) + sin20sin400)
= (sin20sin40sin110)/(sin60cos30)
= sin20sin40sin110/sin60cos30
= sin20sin40sin110/sin60(2sin30cos30)
= sin20sin40sin110/(sin60sin60)
= sin20sin40sin110/(3/4)
= 4/3 sin20sin40sin110
Therefore, the final simplified expression is 4/3 sin20sin40*sin110.