t a n [ 2 t a n − 1 ( 1 5 ) − π 4 ] = Options: A . &nbsp 17 7 B . &nbsp − 17 7 C . &nbsp 7 17 D . &nbsp − 7 17

Answer: Option D : D t a n [ 2 t a n − 1 ( 1 5 ) − π 4 ] = t a n [ t a n − 1 2 5 1 − 1 25 − t a n − 1 ( 1 ) ] = t a n [ t a n − 1 5 12 − t a n − 1 ( 1 ) ] = t a n t a n − 1 ( 5 12 − 1 1 + 5 12 ) = − 7 17

tan[2tan−1(15)−π4]=

Discussion Forum : Inverse Trigonometric Functions

Question -

$t a n [2 t a n^{- 1} (\frac{1}{5}) - \frac{π}{4}] =$

Options:

A .

\frac{17}{7}

B .

- \frac{17}{7}

C .

\frac{7}{17}

D .

- \frac{7}{17}

Answer: Option D
:
D

t a n [2 t a n^{- 1} (\frac{1}{5}) - \frac{π}{4}] = t a n [t a n^{- 1} \frac{\frac{2}{5}}{1 - \frac{1}{25}} - t a n^{- 1} (1)]

= t a n [t a n^{- 1} \frac{5}{12} - t a n^{- 1} (1)] = t a n t a n^{- 1} (\frac{\frac{5}{12} - 1}{1 + \frac{5}{12}}) = - \frac{7}{17}

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