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Given that $ \sin \alpha=\frac{1}{2} $ and $ \cos \beta=\frac{1}{2} $, then the value of $ (\alpha+\beta) $ is
(A) $ 0^{\circ} $
(B) $ 30^{\circ} $
(C) $ 60^{\circ} $
(D) $ 90^{\circ} $
Given:
\( \sin \alpha=\frac{1}{2} \) and \( \cos \beta=\frac{1}{2} \)
To do:
We have to find the value of \( (\alpha+\beta) \).
Solution:
$\sin \alpha =\frac{1}{2}$
$=\sin 30^{\circ}$ [Since \sin 30^{\circ}=\frac{1}{2}$]
This implies,
$\alpha=30^{\circ}$
$\cos \beta =\frac{1}{2}$
$=\cos 60^{\circ}$ [Since \cos 60^{\circ}=\frac{1}{2}$]
This implies,
$\beta=60^{\circ}$
Therefore,
$\alpha+\beta=30^{\circ}+60^{\circ}$
$=90^{\circ}$
The value of \( (\alpha+\beta) \) is $90^{\circ}$.
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