+26367 Compute
\(\cos \left( \dfrac{\pi}{12} \right) + \sin\left( \dfrac{\pi}{12} \right)\).
Formula:
\(\cos \left( x \right) + \sin \left( x \right) =\sqrt{2}\sin \left(x+\dfrac{\pi}{4} \right)\)
\(\begin{array}{|rcll|} \hline \mathbf{\cos \left( \dfrac{\pi}{12} \right) + \sin \left( \dfrac{\pi}{12} \right)} &=& \sqrt{2}\sin \left(\dfrac{\pi}{12}+\dfrac{\pi}{4} \right) \\ &=& \sqrt{2}\sin \left(\dfrac{4\pi}{12} \right) \\ &=& \sqrt{2}\sin \left(\dfrac{\pi}{3} \right) \quad | \quad \sin \left(\dfrac{\pi}{3} \right) = \dfrac{\sqrt{3}}{2} \\ &=& \sqrt{2} \dfrac{\sqrt{3}}{2} \\ &=& \mathbf{\dfrac{\sqrt{6}}{2} } \\ \hline \end{array} \)
