_ 2 ( - )= - Vidyadip

MCQ

$\lim _{\theta \rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)=$

✓
$0$
B
$\frac{1}{2}$
C
2
D
$\infty$

✓

Answer

Correct option: A.

$0$

(A)
$\lim _{\theta \rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)=\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\cos \theta}$
$=\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\left(\cos \frac{\theta}{2}-\sin \frac{\theta}{2}\right)^2}{\left(\cos \frac{\theta}{2}-\sin \frac{\theta}{2}\right)\left(\cos \frac{\theta}{2}+\sin \frac{\theta}{2}\right)}=0$

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