Find the exact value of the expression. $\left( \sin 60 ^ { \circ } \right) ^ { 2 } - \left( \cos 60 ^ { \circ } \right) ^ { 2 }$

A) $\frac { 3 } { 4 }$

B) $\frac { 1 } { 2 }$

C) $\frac { \sqrt { 3 } } { 4 }$

D) $\frac { 3 } { 2 }$

E) $\frac { 1 } { 4 }$

Question

Find the exact value of the expression. $\left( \sin 60 ^ { \circ } \right) ^ { 2 } - \left( \cos 60 ^ { \circ } \right) ^ { 2 }$

A) $\frac { 3 } { 4 }$

B) $\frac { 1 } { 2 }$

C) $\frac { \sqrt { 3 } } { 4 }$

D) $\frac { 3 } { 2 }$

E) $\frac { 1 } { 4 }$

Quizplus · Accepted Answer

The expression simplifies using the identity $\sin^2 \theta - \cos^2 \theta = -\cos 2\theta$. For $\theta = 60^\circ$, $\cos 120^\circ = -\frac{1}{2}$, thus the answer is $\frac{1}{2}$.

Find the Exact Value of the Expression (sin⁡60∘)2−(cos⁡60∘)2\left( \sin 60 ^ { \circ } \right) ^ { 2 } - \left( \cos 60 ^ { \circ } \right) ^ { 2 }(sin60∘)2−(cos60∘)2

Find the Exact Value of the Expression $\left( \sin 60 ^ { \circ } \right) ^ { 2 } - \left( \cos 60 ^ { \circ } \right) ^ { 2 }$