[latex]cos^{8}165 - sin^{8}165[/latex]165 в градусах

[latex]cos^8165-sin^8165=\\ cos^2(\frac{330}{2})^4=\frac{(1+cos330)^4}{16}=\frac{(1+\frac{\sqrt{3}}{2})^4}{16}\\ sin^2(\frac{330}{2})^4=\frac{(1-cos330)^4}{16}=\frac{(1-\frac{\sqrt{3}}{2})^4}{16}\\ \frac{(1+\frac{\sqrt{3}}{2})^4}{16}-\frac{(1-\frac{\sqrt{3}}{2})^4}{16}=\\ [/latex]   [latex]\frac{(1+\frac{\sqrt{3}}{2})^4}{16}-\frac{(1-\frac{\sqrt{3}}{2})^4}{16}=\\ 8*\frac{\sqrt{3}}{2}^3+8*\frac{\sqrt{3}}{2}=3\sqrt{3}+4\sqrt{3}=7\sqrt{3}\\ Otvet \ \frac{7\sqrt{3}}{16} [/latex]