Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
-$$\frac { \sin 52 ^ { \circ } } { 1 + \cos 52 ^ { \circ } }$$
A) $\tan 26 ^ { \circ }$
B) $\cos 26 ^ { \circ }$
C) $\sin 26 ^ { \circ }$
D) $\cot 26 ^ { \circ }$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the trigonometric identity $\sin x = 2 \sin \frac{x}{2} \cos \frac{x}{2}$ and $\cos x = 2 \cos^2 \frac{x}{2} - 1$. Applying these to the given expression, we get $\frac{\sin 52^\circ}{1 + \cos 52^\circ} = \frac{2 \sin 26^\circ \cos 26^\circ}{2 \cos^2 26^\circ}$, which simplifies to $\tan 26^\circ$, making option A correct.

Graph the Expression on Each Side of the Equals Symbol sin⁡52∘1+cos⁡52∘\frac { \sin 52 ^ { \circ } } { 1 + \cos 52 ^ { \circ } }1+cos52∘sin52∘​

Graph the Expression on Each Side of the Equals Symbol $\frac { \sin 52 ^ { \circ } } { 1 + \cos 52 ^ { \circ } }$