Chapter 5 - Section 5.4 - Half-Angle Formulas - 5.4 Problem Set - Page 305: 50

See the steps.

$RHS =\dfrac{\sec{B}}{\sec{B}\csc{B}+\csc{B}} $ Dividing both numerator and denominator by $\sec{B}$ $RHS = \dfrac{1}{\csc{B}+\cot{B}}$ Dividing both numerator and denominator by $\sin{B}$ $RHS = \dfrac{\sin{B}}{1+\dfrac{\cos{B}}{\sin{B}} \sin{B}} = \dfrac{\sin{B}}{1+\cos{B}} = \tan{\dfrac{B}{2}} = LHS$