Question

$sqrt{75} - sqrt{300} sin^2 frac{13Pi}{12}$

Answer 1

$sin^2 alpha =frac{1-cos2 alpha }{2}; to \\sin^2frac{13pi}{12}=sin^2(pi +frac{pi}{12})=sin^2frac{pi}{12}=frac{1-cosfrac{pi}{6}}{2}=frac{1-frac{sqrt3}{2}}{2}=frac{2-sqrt3}{4}\\sqrt{75}-sqrt{300}sin^2frac{13pi }{12}=sqrt{75}(1-2cdot frac{2-sqrt3}{4})=5sqrt3cdot frac{sqrt3}{2}=frac{15}{2}=7,5$