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Question Number 10114 by JAZAR last updated on 24/Jan/17

h o w c a n d e m o n t r e d

\tan 3 x \underset{}{=} \frac{3 t a n x - {t a n}^{3} x}{\underset{}{1} - 3 {t a n}^{2} x}

p l e a c e h e l p m e

Answered by mrW1 last updated on 24/Jan/17

\tan 3 x = \tan (x + 2 x)

= \frac{\tan x + \tan 2 x}{1 - \tan x \tan 2 x}

= \frac{\tan x + \frac{2 \tan x}{1 - \tan^{2} x}}{1 - \tan x \times \frac{2 \tan x}{1 - \tan^{2} x}}

= \frac{\tan x (1 - \tan^{2} x) + 2 \tan x}{1 - \tan^{2} x - {2 \tan}^{2} x}

= \frac{3 \tan x - \tan^{3} x}{1 - {3 \tan}^{2} x}

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