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The quotient of twice the tan function by subtraction of square of tan function from one is simplified as tan of double angle How to use The tangent of double angle identity is used to either expand or simplify the double angle functions like $\tan{2A}$, $\tan{2x}$, $\tan{2\alpha}$ and etc For example, We know from double angle formula that sin 2x = 2 sin x cos x = 2 tan x / (1 tan^2 x) cos 2x = cos^2 x sin^2 x = 1 2 sin^2 x = 2 cos^2 x 1 = 1 tan^2 x / 1 tan^2 x tan 2x = 2 tan x / (1 tan^2 x) These identities can also be used to reduce anglesSum, difference, and double angle formulas for tangent The half angle formulas The ones for sine and cosine take the positive or negative square root depending on the quadrant of the angle θ/2 For example, if θ/2 is an acute angle, then the positive root would be used Truly obscure identities These are just here for perversity No, not Tangent Half Angle Formula Wikipedia Tan 2x double angle formula