trigonometry Proving trig identity $\tan (2x)−\tan (x)=\frac {\tan (x)} {\cos (2x)}$ Mathematics Stack ExchangeWe will use the following trigonometric formula to prove the formula for tan 2x tan (a b) = (tan a tan b)/ (1 tan a tan b) We have tan 2x = tan (x x) = (tan x tan x)/ (1 tan x tan x) = 2 tan x/ (1 tan 2 x) Hence, we have derived the tan 2x formula using the Use the double angle formulas to prove the identity csc 2 θ − cot 2 θ = tan θ \csc 2\theta \cot 2\theta = \tan \theta csc2θ−cot2θ = tanθ We have csc 2 θ − cot 2 θ = 1 sin 2 θ − cos 2 θ sin 2 θ = 1 − cos 2 θ sin 2 θ
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