1) Упростите выражения: [latex]\frac{a^{6}-64}{a^{4}+4a^{2}+16}+\frac{a^{4}-16}{a^{2}+4}[/latex] 2)Вычислите:  [latex]\frac{18}{\pi}*(arctg(-\sqrt{3})+arcsin(-\frac{\sqrt{3}}{2})+arccos(-\frac{\sqrt{3}}{2}))[/latex] 3) Найдите ...

[latex]\frac{a^{6}-64}{a^{4}+4a^{2}+16}+\frac{a^{4}-16}{a^{2}+4}=\frac{(a^2-4)(a^4+4a^2+16)}{a^4+4a^2+16}+\frac{(a^2-4)(a^2+4)}{a^2+4}=2a^2-8[/latex] [latex]\frac{18}{\pi}(\mathrm{arctg}\,(-\sqrt{3})+\arcsin(-\frac{\sqrt{3}}{2})+\arccos(-\frac{\sqrt{3}}{2}))=\frac{18}\pi\cdot(-\frac\pi3+\frac\pi2)=3[/latex] [latex]\sin^{2}(3\mathrm{arctg}\frac{\sqrt{3}}{3}-\arccos\frac{\sqrt{2}}{2})=\sin^2(3\cdot\frac\pi6-\frac\pi4)=\sin^2(\frac\pi4)=\frac12[/latex]

[latex]\frac{(a^2)^3-4^3}{a^4+4a^2+16}+\frac{(a^2)^2-16}{a^2+4}[/latex] 1)a^6-64=(a^2)^3-4^3=(a^2-4)(a^4+4a^2+16) 2)a^4-16=(a^2)^2-4^2=(a^2-4)(a^2+4) Сократив первую и вторую дробь получим:  [latex]a^2-4+a^2-4=2a^2-8[/latex] -------------------------------------------------------------------------------------------- [latex]\frac{18}{\pi}*(arctg(-\sqrt{3})+arcsin(\frac{-\sqrt{3}}{2})+arccos(\frac{-\sqrt{3}}{2}))=\\\frac{18}{\pi}*(-\frac{\pi}{3}-\frac{\pi}{3}+\frac{5\pi}{6})=\frac{18}{\pi}*\frac{\pi}{6}=3[/latex] --------------------------------------------------------------------------------------------- [latex]sin^2(3arctg\frac{\sqrt{3}}{3}-arccos\frac{\sqrt{2}}{2})=sin^2(3\frac{\pi}{6}-\frac{\pi}{4})=sin^2\frac{\pi}{4}=(\frac{\sqrt{2}}{2})^2=0,5[/latex]