Formula for tangent of x by 2 in terms of cosx

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half angle formula for tangent of an angle

\[tan(\frac{x}{2})\]\[=\sqrt{\frac{1-cosx}{1+cosx}}\]

Proof-

 \[ 1-cosx=2sin^2{\frac{x}{2}}\] 

\[ 1+cosx=2cos^2{\frac{x}{2}}\]

RHS=\[\sqrt{\frac{1-cosx}{1+cosx}}=\sqrt{\frac{2sin^2\frac{x}{2}}{2cos^2\frac{x}{2}}}\]=\[ \sqrt{tan^2\frac{x}{2}}=+ or -tan\frac{x}{2}\]