Tg25 градусов + tg35 градусов = ?   

[latex]\tan\alpha+\tan\beta=\tan(\alpha+\beta)*(1-\tan\alpha\tan\beta)[/latex] [latex]\tan25^0+\tan35^0=\tan(25^0+35^0)*(1-\tan25^0\tan35^0)[/latex] [latex]\tan25^0+\tan35^0=\tan60^0*(1-\tan25^0\tan35^0)[/latex] [latex]\tan25^0+\tan35^0=\sqrt{3}*(1-\tan25^0\tan35^0)[/latex]   Отдельно вычислим произведение в скобках по формуле тангенса [latex]\tan\alpha=\frac{\sin\alpha}{\cos\alpha}[/latex]   [latex]\tan25^0\tan35^0=\frac{\sin25^0\sin35^0}{\cos25^0\cos35^0}[/latex] Воспользуемся формулами произведения синусов и косинусов [latex]\sin\alpha\sin\beta=\frac{1}{2}*(\cos(\alpha-\beta)-cos(\alpha+\beta))[/latex]   [latex]\cos\alpha\cos\beta=\frac{1}{2}*(\cos(\alpha-\beta)+cos(\alpha+\beta))[/latex]   [latex]\tan25^0\tan35^0=\frac{\cos(25^0-35^0)-\cos(25^0+35^0)}{\cos(25^0-35^0)+\cos(25^0+35^0)}[/latex]   [latex]\tan25^0\tan35^0=\frac{\cos10^0-\cos60^0}{\cos10^0+\cos60^0}[/latex]   [latex]\tan25^0\tan35^0=\frac{\cos10^0-0,5}{\cos10^0+0,5}[/latex]   [latex]1-\tan25^0\tan35^0=1-\frac{\cos10^0-0,5}{\cos10^0+0,5}[/latex]   [latex]1-\frac{\cos10^0-0,5}{\cos10^0+0,5}=\frac{\cos10^0+0,5-\cos10^0+0,5}{\cos10^0+0,5}[/latex]   [latex]\frac{\cos10^0+0,5-\cos10^0+0,5}{\cos10^0+0,5}=\frac{1}{\cos10^0+0,5}[/latex]   [latex]\tan25^0+\tan35^0=\sqrt{3}*\frac{1}{\cos10^0+0,5}[/latex]   [latex]\tan25^0+\tan35^0=\frac{\sqrt{3}}{\cos10^0+0,5}[/latex]