Докажите равенство [latex]\displaystyle \frac{\sin50^\circ+\cos50^\circ}{\sqrt{2}\sin85^\circ}=1;\\ \frac{\cos40^\circ-\sqrt{3}\sin40^\circ}{\sin190^\circ}=2[/latex]

[latex]1)\quad \frac{sin50+cos50}{\sqrt2sin95} = [\, cos50=cos(90-40)=sin40]=\\\\=\frac{sin50+sin40}{\sqrt2sin(90-5)} = \frac{2sin45\cdot cos5}{\sqrt2cos5} = \frac{2\cdot \frac{\sqrt2}{2}}{\sqrt2} = \frac{2\sqrt2}{2\sqrt2} =1\\\\2)\quad \frac{cos40-\sqrt3sin40}{sin190} = \frac{2(\frac{1}{2}cos40-\frac{\sqrt3}{2}sin40)}{sin(180+10)} = \frac{2(sin30\cdot cos40-cos30\cdot sin40)}{-sin10} =\\\\= \frac{2\cdot sin(30-40)}{-sin10} = -\frac{2sin(-10)}{-sin10} = \frac{2sin10}{sin10} =2[/latex]