If + = p, then is equal to - Vidyadip

MCQ

If $\sec \theta + \tan \theta = p,$ then $\tan \theta $ is equal to

A
$\frac{{2p}}{{{p^2} - 1}}$
✓
$\frac{{{p^2} - 1}}{{2p}}$
C
$\frac{{{p^2} + 1}}{{2p}}$
D
$\frac{{2p}}{{{p^2} + 1}}$

✓

Answer

Correct option: B.

$\frac{{{p^2} - 1}}{{2p}}$

b
(b) $\sec \theta + \tan \theta = p\,\, $........$(i)$

$\Rightarrow \,\sec \,\theta - \tan \theta = \frac{1}{p}$..........$(ii)$

Subtracting second from first, we get

$2\tan \theta = p - \frac{1}{p}$

$ \Rightarrow \,\tan \theta = \frac{{{p^2} - 1}}{{2p}}$.

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