<span>Apply the half angle formula to convert tan(B/2) to terms of B: </span> <span>sin(B) / (1+cos(B)) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Convert everything else to be in terms of sin and cos: </span> <span>sin(B) / (1+cos(B) = (1/cos(B)) / ((1/cos(B)) * (1/sin(B)) + (1/sin(B))) </span>
<span>Multiply right side by "sin(B)/sin(B)" to simplify the fractions: </span> <span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + 1) </span>
<span>Change "1" to cos(B)/cos(B) and then combine over </span> <span>common denominator: </span> <span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + cos(B)/cos(B)) </span> <span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1+cos(B))/cos(B)) </span>
<span>Dividing by a fraction equals multiplying by its reciprocal: </span> <span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) * (cos(B) / (1+cos(B))) </span>
<span>Multiply terms on the right side (canceling cos(B) terms): </span> <span>sin(B) / (1+cos(B) = sin(B) / (1+cos(B)) </span>
It will take 4 days in all to eat all of the raisins because if you eat 1/8 of raisins every day for 4 days that’s 4x1/8 which would equal 4/8, and 4/8 is equal to 1/2. So you have your answer :)