Use Sum and Difference Formulas for Cosines and Sines
-$\cos 15 ^ { \circ } \cos 45 ^ { \circ } - \sin 15 ^ { \circ } \sin 45 ^ { \circ }$
A) $\frac { 1 } { 2 }$
B) $\frac { \sqrt { 3 } } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\sqrt { 3 }$

Question

Quizplus · Accepted Answer

This expression can be simplified using the cosine of sum formula, $\cos(A + B) = \cos A \cos B - \sin A \sin B$, which directly applies here with $A = 15^\circ$ and $B = 45^\circ$. Thus, it simplifies to $\cos(15^\circ + 45^\circ) = \cos(60^\circ)$, which equals $\frac{1}{2}$.

Use Sum and Difference Formulas for Cosines and Sines - cos⁡15∘cos⁡45∘−sin⁡15∘sin⁡45∘\cos 15 ^ { \circ } \cos 45 ^ { \circ } - \sin 15 ^ { \circ } \sin 45 ^ { \circ }cos15∘cos45∘−sin15∘sin45∘

Use Sum and Difference Formulas for Cosines and Sines
- $\cos 15 ^ { \circ } \cos 45 ^ { \circ } - \sin 15 ^ { \circ } \sin 45 ^ { \circ }$