Find the exact value of the expression.
-$\sin \left( \cos ^ { - 1 } \frac { 1 } { 2 } - \sin ^ { - 1 } \frac { \sqrt { 3 } } { 2 } \right)$
A) 0
B) $\frac { \sqrt { 3 } } { 3 }$
C) $\frac { 2 \sqrt { 3 } } { 2 }$
D) 1

Question

Quizplus · Accepted Answer

The expression simplifies to $\sin(60^\circ - 30^\circ) = \sin(30^\circ) = \frac{1}{2}$. However, none of the options correctly matches this value, indicating a mistake in my response based on the provided options. The correct approach involves recognizing the angles associated with the given trigonometric values and applying trigonometric identities correctly.

Find the Exact Value of the Expression sin⁡(cos⁡−112−sin⁡−132)\sin \left( \cos ^ { - 1 } \frac { 1 } { 2 } - \sin ^ { - 1 } \frac { \sqrt { 3 } } { 2 } \right)sin(cos−121​−sin−123​​)

Find the Exact Value of the Expression $\sin \left( \cos ^ { - 1 } \frac { 1 } { 2 } - \sin ^ { - 1 } \frac { \sqrt { 3 } } { 2 } \right)$