Тригонометрия !!!!!!!!последний пример

[latex](1-cos2x)ctgx=sinx \\ ctgx= \frac{cosx}{sinx} \\ cos2x=cos^{2}x-sin^{2}x \\ (1-( cos^{2}x-sin^{2}x) \frac{cosx}{sinx} =sinx \\ (1- cos^{2}x+sin^{2}x) {cosx} =sin^{2}x \\ cos^{2}x+sin^{2}x=1 \\ (1-1)cosx=sin^{2}x \\ sin^{2}x =0 \\ x= \pi + \pi k [/latex]