Question

Rezultatul calcului sin 60 + sin 30/ cos 30- cos 60 este

Answer 1

      
[tex]\displaystyle \frac{sin \;60 + sin\; 30}{cos\;30- cos \;60} = \\ \\ =\frac{ \frac{ \sqrt{3} }{2} + \frac{1}{2}}{\frac{ \sqrt{3} }{2}- \frac{1}{2}}= \\ \\ =\frac{\frac{1}{2}( \sqrt{3}+ 1)}{\frac{1}{2}( \sqrt{3}- 1)}= \\ \\ =\frac{ \sqrt{3}+ 1}{ \sqrt{3}- 1}= ~~~~~ (rationalizam~numitorul) \\ \\ =\frac{ (\sqrt{3}+ 1)(\sqrt{3}+ 1)}{ (\sqrt{3}- 1)(\sqrt{3}+ 1)} = \frac{3+2\sqrt{3}+1}{3-1}= \frac{4+2\sqrt{3}}{2} = \boxed{2+\sqrt{3}}[/tex]