Use an Identity to Write the Expression as a Single $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$

Multiple Choice

Use an identity to write the expression as a single trigonometric function or as a single number.
-Use the exact value $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$ and identities to find the exact value of $\sin 72 ^ { \circ }$ .

A) $\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( 5 + 3 \sqrt { 5 } ) } { 40 }$
B) $\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( \sqrt { 5 } - 1 ) } { 4 }$
C) $\frac { \sqrt { 10 + 2 \sqrt { 5 } } } { 4 }$
D) $\frac { \sqrt { 10 + \sqrt { 5 } } } { 8 }$