Simplify this expression...?

Question

I need help simplifying this expression so that it involves a function of only one angle.

sin 130° + sin 20°/cos 130° + cos 20°

please show your work. Thanks!

Answer 1

(sin 130 + sin 20) / (cos 130 + cos 20)

= [ 2sin(150 / 2)cos(90 / 2) ] /  [ 2 cos(150 /  2)cos(110 / 2) ]

= [ sin(75)cos(45) ] / [ cos(75)cos(45) ]

= sin(75) / cos(75)

= tan(75).