Hello from MrBillDoesMath!
Answer:
cos (pi/3 + B) = 1/2( cosB - sqrt(3) sinB)
the first item in the list.
Discussion:
The standard double-angle formula for cos is:
cos (A + B) = cosAcosB - sinAsinB
Applying this formula to cos (pi/3 + B ) gives
cos(pi/3 + B) = cos(pi/3)cosB - sin(pi/3)sinB
But cos(pi/3) = cos (180/3) = cos(60) = 1/2 and
sin(pi/3) = sqrt(3)/2
Substituting these values gives
cos (pi/3 + B) = 1/2 cosB - sqrt(3)/2 sinB =
1/2( cosB - sqrt(3) sinB)
which is the first answer.
Regards,
MrB
