Answer:
sin(13π/40)
Step-by-step explanation:
The given expression matches the pattern ...
sin(a)cos(b) +cos(a)sin(b) = sin(a+b)
Then ...
sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)
= sin(13π/40)
_____
π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)
