If + = e^x , then equals - Vidyadip

MCQ

If $\tan \theta + \sec \theta = {e^x},$ then $\cos \theta $ equals

A
$\frac{{({e^x} + {e^{ - x}})}}{2}$
✓
$\frac{2}{{({e^x} + {e^{ - x}})}}$
C
$\frac{{({e^x} - {e^{ - x}})}}{2}$
D
$\frac{{({e^x} - {e^{ - x}})}}{{({e^x} + {e^{ - x}})}}$

✓

Answer

Correct option: B.

$\frac{2}{{({e^x} + {e^{ - x}})}}$

b
(b) $\tan \theta + \sec \theta = {e^x}$…..$(i)$

$\therefore \,\,\,\sec \theta - \tan \theta = {e^{ - x}}$…..$(ii)$

From $(i)$ and $(ii),$

$\,2\sec \theta = {e^x} + {e^{ - x}}\,$

$\Rightarrow \,\cos \theta = \frac{2}{{{e^x} + {e^{ - x}}}}.$

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