If = t, then 2 + 2 = - Vidyadip

MCQ

If $\tan \theta = t,$ then $\tan 2\theta + \sec 2\theta = $

✓
$\frac{{1 + t}}{{1 - t}}$
B
$\frac{{1 - t}}{{1 + t}}$
C
$\frac{{2t}}{{1 - t}}$
D
$\frac{{2t}}{{1 + t}}$

✓

Answer

Correct option: A.

$\frac{{1 + t}}{{1 - t}}$

a
(a) $\tan 2\theta = \frac{{2\tan \theta }}{{1 - {{\tan }^2}\theta }},\cos 2\theta = \frac{{1 - {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }}$

$\tan 2\theta + \sec 2\theta = \frac{{2t}}{{1 - {t^2}}} + \frac{{1 + {t^2}}}{{1 - {t^2}}} $

$= \frac{{{{(1 + t)}^2}}}{{(1 - t)(1 + t)}} = \frac{{1 + t}}{{1 - t}}$.

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