Answer:
Using the trigonometric identity,
cos(A+B) = cosAcosB - sinAsinB
cos 30° + cos 60° + cos 290° + 2 cos 30° cos 60° cos 90°
= cos 30° + cos 60° + cos (360° - 70°) + 2 cos 30° cos 60° (0)
= cos 30° + cos 60° + cos 70°
= √3/2 + 1/2 + cos 70°
Using the identity,
cos(90° - A) = sinA
cos 70° = sin(90° - 70°) = sin20°
√3/2 + 1/2 + cos 70° = √3/2 + 1/2 + sin20°
Therefore, the final answer is √3/2 + 1/2 + sin20°.