Решить уравнения 1)1+сosx=sinx 2)tgx-tg4x=0

[latex]1+cos x=sin x \ cos^2 frac{x}{2} +sin^2frac{x}{2}+cos^2frac{x}{2}-sin^2frac{x}{2}=2sinfrac{x}{2}cosfrac{x}{2} \ 2cos^2frac{x}{2}-2sinfrac{x}{2}cosfrac{x}{2}=0 \ 2cosfrac{x}{2}(cosfrac{x}{2}-sinfrac{x}{2})=0 \ left[egin{array}{ccc}cos frac{x}{2}=0 \ tgfrac{x}{2}=1end{array}ighto left[egin{array}{ccc}frac{x}{2}= frac{pi}{2}+pi n,n in Z \ frac{x}{2}= frac{ pi }{4} + pi n,n in Z end{array}ighto [/latex][latex]oleft[egin{array}{ccc}x= pi +2 pi n,nin Z\ x= frac{pi}{2}+2 pi n,n in Z end{array}ight[/latex][latex]tgx-tg4x=0 \ frac{sin(x-4x)}{cos xcos 4x} =0 \ \ frac{-sin3x}{cos xcos 4x}=0 \ \ sin 3x=0 \ 3x=pi k,k in Z \ x= frac{pi k}{3} ,k in Z[/latex]