sin z/1+cos z=2-ctg z

Question

sin z/1+cos z=2-ctg z

Answer 1

2sinz/2cosz/2/(2cos^2z/2)=tgz/2

2-(1-tg^2z/2)/2tgz/2

tgz/2=u

 

u=2-(1-u^2)/2u

-u^2+4u-1=0

u^2-4u+1=0

2+-sqrt(3)

z=2arctg(2+-sqrt(3))+2Пk