(1+sinx+cosx)/(1+sinx-cosx)=ctg(x/2);
(1+sin(π/2-x)+sinx)/(1+sinx-sin(π/2-x))=(1+2*sin(π/4)*cos(π/4-x))/(1+2*sin(x-π/4)*cos(π/4))=(1+√2*cos(π/4-x))/(1+√2*sin(π/4-x))=ctg(x/2). - доказанно.
тождество доказано
(1+sinx+cosx)/(1+sinx-cosx)=ctg(x/2);
(1+sin(π/2-x)+sinx)/(1+sinx-sin(π/2-x))=(1+2*sin(π/4)*cos(π/4-x))/(1+2*sin(x-π/4)*cos(π/4))=(1+√2*cos(π/4-x))/(1+√2*sin(π/4-x))=ctg(x/2). - доказанно.