Q-If-tan-pi-4-1-2-Find-the-value-of-tan-4-

Question Number 200040 by mnjuly1970 last updated on 12/Nov/23

Q : I f, t a n (\frac{π}{4} - α) = \frac{1}{2}

\Rightarrow F i n d t h e v a l u e o f, t a n (4 α) = ?

Answered by witcher3 last updated on 12/Nov/23

\Rightarrow tg (π - 4 α) = - tg (4 α)

tg (4 x) . \frac{2 tg (2 x)}{1 - {tg}^{2} (2 x)} = \frac{2 . \frac{2 tg (x)}{1 - {tg}^{2} (x)}}{1 - {(\frac{2 tg (x)}{1 - {tg}^{2} (x)})}^{2}}

tg (4 (\frac{π}{4} - α) = \frac{2 \frac{2 . \frac{1}{2}}{1 - {(\frac{1}{2})}^{2}}}{1 - {(\frac{1}{1 - {(\frac{1}{2})}^{2}})}^{2}} = \frac{\frac{8}{3}}{1 - \frac{16}{9}} = - \frac{24}{7} = - tg (4 a)

tg (4 a) = \frac{24}{7}

Commented by mnjuly1970 last updated on 13/Nov/23

t h x a l o t \dots

Answered by des_ last updated on 12/Nov/23

\frac{1 - \tan (α)}{1 + \tan (α)} = \frac{1}{2} \Rightarrow \tan (α) = \frac{1}{3};

\tan (2 α) = \frac{2 \tan (α)}{1 - \tan^{2} (α)} = \frac{3}{4};

\tan (4 α) = \frac{2 \tan (2 α)}{1 - \tan^{2} (2 α)} = \frac{24}{7}

Commented by mnjuly1970 last updated on 13/Nov/23

t h x a l o t