simplify : (sin80°-sin10°)/(sin 80°+sin10°) and (sin 130° + sin20° ) / (sin 130° + cos 20° )?

Question

so that they involve a function of only one angle.

Answer 1

For the first one:

sin80 - sin10 = sin(45+35) - sin(45-35) = 2.cos45.sin35 [1]
sin80 +sin10 = sin(45+35) + sin(45-35)=2.sin45.cos35 [2]

Hence the expression you give equals [1] / [2] = tan35