The challenge trignometry question is: simplify $sin (80^\circ) + sin (40^\circ) $ using trignometric identities. All the angle values are in degrees.
This is what I did: Let $a=40^\circ$. So we have $sin(2a) +sin(a)$. Using the formula for $sin(2a)$, I have, $$2sin(a)cos(a) + sin(a)=sin(40)(2cos(40^\circ)+1)$$
All I got was a big red mark through the question. I looked at co-functions and half-angles and couldn't find a solution that came out to something I could do without a calculator. Any thoughts?