If = - 3 5 , where < < 3 2 , then 1 2 = - Vidyadip

MCQ

If $\sin \alpha = \frac{{ - 3}}{5},$ where $\pi < \alpha < \frac{{3\pi }}{2},$ then $\cos \frac{1}{2}\alpha = $

✓
$\frac{{ - 1}}{{\sqrt {10} }}$
B
$\frac{1}{{\sqrt {10} }}$
C
$\frac{3}{{\sqrt {10} }}$
D
$\frac{{ - 3}}{{\sqrt {10} }}$

✓

Answer

Correct option: A.

$\frac{{ - 1}}{{\sqrt {10} }}$

a
(a) $\cos (\alpha /2) = - \sqrt {\frac{{1 + \cos \alpha }}{2}} $

$\cos \alpha = - \sqrt {1 - {{\sin }^2}\alpha } $ [$\because \alpha$ lies in $III^{rd}$ Quadrant]

$ = - \sqrt {1 - \frac{9}{{25}}} = - \frac{4}{5}$

$\therefore \,\,\,\cos (\alpha /2) = - \sqrt {\frac{{1 - \frac{4}{5}}}{2}} = - \frac{1}{{\sqrt {10} }}$.

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