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} $

AcademicMathematicsNCERTClass 10

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 $90^{\circ}$.

raja
Updated on 10-Oct-2022 13:28:52

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