Solve the problem.
-$\cos \left( - 75 ^ { \circ } \right)$
A) $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$
B) $\sqrt { 2 } - \sqrt { 6 }$
C) $- \sqrt { 6 } - \sqrt { 2 }$
D) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The cosine function is even, meaning $\cos(-x) = \cos(x)$. Therefore, $\cos(-75^\circ) = \cos(75^\circ)$. Using the half-angle identity, $\cos(75^\circ) = \cos(30^\circ/2)$, we can find that $\cos(75^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}$, making option D correct.

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