Упростить выражение: (1+ctg2x*ctgx)/(tgx+ctgx) 1)tg2x 2)0,5ctgx 3)cos2x 4)sin2x

[latex] \frac{1+ctg2x\cdot ctgx}{tgx+ctgx} = \frac{1+\frac{cos2x}{sin2x}\cdot \frac{cosx}{sinx}}{\frac{sinx}{cosx}+\frac{cosx}{sinx}} = \frac{sin2x\cdot sinx+cos2x\cdot cosx}{sin2x\cdot sinx\cdot \frac{sin^2x+cos^2x}{sinx\cdot cosx}} =\\\\= \frac{cos(2x-x)}{2sinx\cdot cosx\cdot \frac{1}{cosx}} = \frac{cosx}{2sinx} =\frac{1}{2}ctgx[/latex]