Найдите значение выражения[latex] sqrt{108} cos^{2} ( frac{13 pi }{12} )- sqrt{27} [/latex]

[latex] sqrt{108}cos^2 frac{13 pi }{12}- sqrt{27}=sqrt{108}cos^2( pi+ frac{pi}{12})}- sqrt{27}= \ sqrt{108}cos^2(-frac{pi}{12})}- sqrt{27}=sqrt{108}* frac{1+cosfrac{pi}{6}}{2}- sqrt{27}= \ sqrt{108}* frac{1+frac{ sqrt{3}}{2}}{2}- sqrt{27}=sqrt{4*27}* frac{2+ sqrt{3}}{4}}- sqrt{27}= \ sqrt{27}* frac{2+ sqrt{3}}{2}}- sqrt{27}=sqrt{27}( frac{2+ sqrt{3}}{2}}-1)=sqrt{27} frac{2+ sqrt{3}-2}{2}= frac{ sqrt{27}* sqrt{3}}{2}= \ frac{ sqrt{3*3^3}}{2}= frac{9}{2}=4.5 [/latex]