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)
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)