Use Sum and Difference Formulas for Cosines and Sines
-$\cos \left( 30 ^ { \circ } + 45 ^ { \circ } \right)$
A) $\frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$
B) $\frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$
C) $- \frac { \sqrt { 2 } ( \sqrt { 3 } - 1 ) } { 4 }$
D) $- \frac { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } { 4 }$

Question

Quizplus · Accepted Answer

Using the sum formula for cosines, we have:$\cos (30^\circ + 45^\circ) = \cos 30^\circ \cos 45^\circ - \sin 30^\circ \sin 45^\circ$Substituting the values of $\cos 30^\circ$, $\cos 45^\circ$, $\sin 30^\circ$, and $\sin 45^\circ$, we get:$\cos (30^\circ + 45^\circ) = \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} - \frac{1}{2} \cdot \frac{1}{\sqrt{2}}$Simplifying, we get:$\cos (30^\circ + 45^\circ) = \frac{\sqrt{3} - 1}{2\sqrt{2}}$Dividing both the numerator and denominator by $\sqrt{2}$, we get:$\cos (30^\circ + 45^\circ) = \frac{\sqrt{2} (\sqrt{3} - 1)}{4}$Therefore, the correct answer is A.

Use Sum and Difference Formulas for Cosines and Sines - cos⁡(30∘+45∘)\cos \left( 30 ^ { \circ } + 45 ^ { \circ } \right)cos(30∘+45∘)

Use Sum and Difference Formulas for Cosines and Sines
- $\cos \left( 30 ^ { \circ } + 45 ^ { \circ } \right)$