Find the exact value of cos 105 degrees. In simpliest form.
+118724 Find the exact value of cos 105 degrees. In simpliest form.
\(cos(60+45)\\ =cos60cos45 - sin60sin45\\ =\frac{1}{2}*\frac{1}{\sqrt{2}}\;\;-\;\;\frac{\sqrt3}{2}*\frac{1}{\sqrt2}\\ =\frac{1}{2\sqrt{2}}\;\;-\;\;\frac{\sqrt3}{2\sqrt2}\\ =\frac{\sqrt2}{4}\;\;-\;\;\frac{\sqrt6}{4}\\ =\frac{\sqrt2-\sqrt6}{4}\\\)
+118724 Find the exact value of cos 105 degrees. In simpliest form.
\(cos(60+45)\\ =cos60cos45 - sin60sin45\\ =\frac{1}{2}*\frac{1}{\sqrt{2}}\;\;-\;\;\frac{\sqrt3}{2}*\frac{1}{\sqrt2}\\ =\frac{1}{2\sqrt{2}}\;\;-\;\;\frac{\sqrt3}{2\sqrt2}\\ =\frac{\sqrt2}{4}\;\;-\;\;\frac{\sqrt6}{4}\\ =\frac{\sqrt2-\sqrt6}{4}\\\)
