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Half-Angle Identities

$\displaystyle \left.\begin{aligned}& \sin\frac{x}{2}=\pm\sqrt{\frac{1-\cos x}{2... ...{\sin x}{1+\cos x}=\pm\sqrt{\frac{1-\cos x}{1+\cos x}} & \end{aligned} \right\}$   Sign is determined by quadrant in which $ \frac{x}{2}$ lies.      

  $\displaystyle \sin^2x=\frac{1-\cos 2x}{2}$   $\displaystyle \cos^2x=\frac{1+\cos 2x}{2}$   $\displaystyle \tan^2x=\frac{1-\cos 2x}{1+\cos 2x}$      



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