Các công thức góc chia đôi

   Các công thức góc chia đôi:

• \(sin\dfrac{\alpha}{2}= \pm \sqrt{\dfrac{1-cos\alpha}{2}}\)
• \(cos\dfrac{\alpha}{2}= \pm \sqrt{\dfrac{1+ cos\alpha}{2}}\)
• \(tan\dfrac{\alpha}{2}= \dfrac{sin\alpha}{1+cos\alpha}= \dfrac{1-cos\alpha}{sin\alpha}= \pm \sqrt{\dfrac{1- cos\alpha}{1+cos\alpha}}\)
• \(cot\dfrac{\alpha}{2}= \dfrac{sin\alpha}{1-cos\alpha}= \dfrac{1+cos\alpha}{sin\alpha}= \pm \sqrt{\dfrac{1+cos\alpha}{1-cos\alpha}}\)
• \(sin\alpha= \dfrac{2tan\dfrac{\alpha}{2}}{1+tan^2\dfrac{\alpha}{2}}\)
• \(cos\alpha= \dfrac{1-tan^2\dfrac{\alpha}{2}}{1+ tan^2\dfrac{\alpha}{2}}\)
• \(tan\alpha=\dfrac{2tan\dfrac{\alpha}{2}}{1-tan^2\dfrac{\alpha}{2}}\)
• \(\vert{cos\alpha\pm sin\alpha}\vert= \sqrt{1+sin2\alpha}\)
• \(1+cos\alpha= 2cos^2\dfrac{\alpha}{2}\)
• \(1-cos\alpha= 2sin^2\dfrac{\alpha}{2}\)
• \(1+sin\alpha= (sin\dfrac{\alpha}{2}+ cos\dfrac{\alpha}{2})^2= 2cos^2(\dfrac{\pi}{4}- \dfrac{\alpha}{2})\)
• \(1 -sin\alpha=(sin\dfrac{\alpha}{2}-cos\dfrac{\alpha}{2})^2=2sin^2(\dfrac{\pi}{4}-\dfrac{\alpha}{2})\)