Find the exact value of the expression. Do not use a calculator.
-$\cot 45 ^ { \circ } - \sin 60 ^ { \circ }$
A) $\frac { 2 - \sqrt { 3 } } { 2 }$
B) $- \frac { \sqrt { 3 } } { 6 }$
C) $\frac { 2 - \sqrt { 2 } } { 2 }$
D) $\frac { 2 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$

Question

Quizplus · Accepted Answer

$\cot 45^\circ = 1$ because $\cot$ is the reciprocal of $\tan$, and $\tan 45^\circ = 1$. $\sin 60^\circ = \frac{\sqrt{3}}{2}$. Therefore, the expression simplifies to $1 - \frac{\sqrt{3}}{2} = \frac{2 - \sqrt{3}}{2}$.

Find the Exact Value of the Expression cot⁡45∘−sin⁡60∘\cot 45 ^ { \circ } - \sin 60 ^ { \circ }cot45∘−sin60∘

Find the Exact Value of the Expression $\cot 45 ^ { \circ } - \sin 60 ^ { \circ }$