Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.
-$2 \sin 75 ^ { \circ } \cos 75 ^ { \circ }$
A) $\frac { 1 } { 2 }$
B) $- \frac { \sqrt { 3 } } { 2 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

The expression $2 \sin 75 ^ { \circ } \cos 75 ^ { \circ }$ can be rewritten using the double angle formula for sine, which is $\sin(2\theta) = 2 \sin(\theta) \cos(\theta)$. Therefore, $2 \sin 75 ^ { \circ } \cos 75 ^ { \circ } = \sin(150^\circ)$. The exact value of $\sin(150^\circ)$ is $\frac{1}{2}$, which corresponds to choice A.

Write the Expression as the Sine, Cosine, or Tangent of a Double