If x = + , then x + 1 x = - Vidyadip

MCQ

If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $

A
$1$
✓
$2\sec \theta $
C
$2$
D
$2\tan \theta $

✓

Answer

Correct option: B.

$2\sec \theta $

b
(b) Given that $x = \sec \theta + \tan \theta $

$ \Rightarrow \,x + \frac{1}{x} = \sec \theta + \tan \theta + \frac{1}{{\sec \theta + \tan \theta }}$

$ = \sec \theta + \tan \theta + \sec \theta - \tan \theta = 2\sec \theta $

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