cos(3π/7 + π/14)

Applying the sum of angles formula for cosine: cos(A+B) = cosAcosB - sinAsinB

we have:

cos(3π/7 + π/14) = cos(3π/7)cos(π/14) - sin(3π/7)sin(π/14)

= cos(3π/7)cos(π/14) - sin(3π/7)sin(π/14)

= (cos(3π/7)cos(π/14) - sin(3π/7)sin(π/14))

Therefore, sin(3π/7)cos(π/14) + cos(3π/7)sin(π/14) = cos(3π/7 + π/14)