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t=\tan\frac{x}{2}
\sin x=\frac{2t}{1+t^2}\ ,\ \ \cos x=\frac{1-t^2}{1+t^2}\ ,\ \ \frac{dx}{dt}=\frac{2}{1+t^2}
\cot x=\frac{1}{\tan x}\ ,\ \ \csc x=\frac{1}{\sin x}\ ,\ \ \sec x=\frac{1}{\cos x}
\sqrt{z},\sqrt{\overline{z}}
z,\overline{z}