### 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=$\sqrt{\frac{1-cosx}{1+cosx}}=\sqrt{\frac{2sin^2\frac{x}{2}}{2cos^2\frac{x}{2}}}$=$\sqrt{tan^2\frac{x}{2}}=+ or -tan\frac{x}{2}$