If = 11 4 , then 2 = - Vidyadip

MCQ

If $\sec \theta = 1\frac{1}{4}$, then $\tan \frac{\theta }{2} = $

✓
$\frac{1}{3}$
B
$\frac{3}{4}$
C
$\frac{1}{4}$
D
$\frac{5}{4}$

✓

Answer

Correct option: A.

$\frac{1}{3}$

a
(a) Given that $\sec \theta = \frac{5}{4}$

$\sec \theta = \frac{{1 + {{\tan }^2}(\theta /2)}}{{1 - {{\tan }^2}(\theta /2)}} $

$\Rightarrow \frac{5}{4} = \frac{{1 + {{\tan }^2}(\theta /2)}}{{1 - {{\tan }^2}(\theta /2)}}$

==> $5 - 5{\tan ^2}(\theta /2) = 4 + 4{\tan ^2}(\theta /2)$

==> $9{\tan ^2}(\theta /2) = 1\, $

$\Rightarrow \tan (\theta /2) = \frac{1}{3}$.

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