For A = 133^ , ;2 A 2 is equal to - Vidyadip

MCQ

For $A = 133^\circ ,\;2\cos \frac{A}{2}$ is equal to

A
$ - \sqrt {1 + \sin A} - \sqrt {1 - \sin A} $
B
$ - \sqrt {1 + \sin A} + \sqrt {1 - \sin A} $
✓
$\sqrt {1 + \sin A} - \sqrt {1 - \sin A} $
D
$\sqrt {1 + \sin A} + \sqrt {1 - \sin A} $

✓

Answer

Correct option: C.

$\sqrt {1 + \sin A} - \sqrt {1 - \sin A} $

c
(c) For $A = {133^o},\frac{A}{2} = {66.5^o}$

==> $\sin \frac{A}{2} > \cos \frac{A}{2} > 0$

Hence, $\sqrt {1 + \sin A} = \sin \frac{A}{2} + \cos \frac{A}{2}$…..$(i)$

and $\sqrt {1 - \sin A} = \sin \frac{A}{2} - \cos \frac{A}{2}$…..$(ii)$

Subtract $(ii)$ from $(i)$, $2\cos \frac{A}{2} = \sqrt {1 + \sin A} - \sqrt {1 - \sin A} $.

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