# Trigonometry - Half angle formulas

1. $sin{\alpha \over 2 }= \pm\sqrt {1-cos\alpha \over 2 }$

2. $cos{\alpha \over 2 }= \pm\sqrt {1+cos\alpha \over 2 }$

3. $tan{\alpha \over 2}=\pm \sqrt {1-cos\alpha \over1+cos\alpha}={sin\alpha \over1+cos \alpha}={1-cos\alpha \over sin\alpha}= cosec\alpha-cot\alpha$

4. $cot{\alpha \over 2}=\pm \sqrt {1+cos\alpha \over 1-cos\alpha}={sin\alpha \over1-cos\alpha}={1+cos\alpha \over sin\alpha}=cosec\alpha+cot\alpha$