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