( 4 + ) - ( 4 - ) = - Vidyadip

MCQ

$\tan \left( {\frac{\pi }{4} + \theta } \right) - \tan \left( {\frac{\pi }{4} - \theta } \right) = $

✓
$2\tan 2\theta $
B
$2\cot 2\theta $
C
$\tan 2\theta $
D
$\cot 2\theta $

✓

Answer

Correct option: A.

$2\tan 2\theta $

a
(a) $\tan \left( {\frac{\pi }{4} + \theta } \right) - \tan \left( {\frac{\pi }{4} - \theta } \right) $

$= \frac{{1 + \tan \theta }}{{1 - \tan \theta }} - \frac{{1 - \tan \theta }}{{1 + \tan \theta }}$

$ = \frac{{4\tan \theta }}{{1 - {{\tan }^2}\theta }} $

$= 2\left( {\frac{{2\tan \theta }}{{1 - {{\tan }^2}\theta }}} \right) $

$= 2\tan 2\theta $.

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