Use a double-angle formula or half-angle formula to simplify $\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }$
A) $\tan 48 ^ { \circ }$
B) $\tan 24 ^ { \circ }$
C) $\csc 24 ^ { \circ }$
D) $\frac { 1 } { \tan 48 ^ { \circ } }$
E) $1 + \sin 24 ^ { \circ }$

Question

Quizplus · Accepted Answer

Using the half-angle formula, we have:
\begin{align*}
\frac{\sin 48^\circ}{1+\cos 48^\circ} &= \frac{2\sin \frac{48^\circ}{2}\cos \frac{48^\circ}{2}}{1+2\cos^2 \frac{48^\circ}{2}-1} \
&= \frac{2\sin 24^\circ \cos 24^\circ}{2\cos^2 24^\circ} \
&= \frac{\sin 24^\circ}{\cos 24^\circ} \
&= 	an 24^\circ.
\end{align*} Thus, the best choice is $\boxed{	extbf{(B)}}.$

Use a Double-Angle Formula or Half-Angle Formula to Simplify sin⁡48∘1+cos⁡48∘\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }1+cos48∘sin48∘​

Use a Double-Angle Formula or Half-Angle Formula to Simplify $\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }$