Half-angle formulas

Half angle identities:

• $\sin {\left({\frac {x}{2}}\right)}=\pm {\sqrt {\frac {1-\cos {x}}{2}}}$

• $\cos {\left({\frac {x}{2}}\right)}=\pm {\sqrt {\frac {1+\cos {x}}{2}}}$

• $\tan {\left({\frac {x}{2}}\right)}=\pm {\sqrt {\frac {1-\cos {x}}{1+\cos {x}}}}$

$={\frac {\sin {x}}{1+\cos {x}}}$

$={\frac {1-\cos {x}}{\sin {x}}}$

Resources

• Half-angle formulas. Written notes created by Professor Esparza, UTSA.