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Compute cos(pi/12) + sin(pi/12).

 May 19, 2020
 #1
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Compute
\(\cos \left( \dfrac{\pi}{12} \right) + \sin\left( \dfrac{\pi}{12} \right)\).

 

Formula:

\(\cos \left( x \right) + \sin \left( x \right) =\sqrt{2}\sin \left(x+\dfrac{\pi}{4} \right)\)

 

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

 

laugh

 May 19, 2020

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