Question : If $\sin \alpha=\frac12$ and $\sin \beta=\frac12$, then what is the value of $\cos (\alpha+\beta)$? $(0°<\alpha, \beta<90° )$
Option 1: $\frac{\sqrt{3}}{2}$
Option 2: $\frac{1}{ 4}$
Option 3: $\frac12$
Option 4: $1$
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Correct Answer: $\frac12$
Solution :
Given,
$\sin \alpha=\frac12$ and $\sin \beta=\frac12$ and $0°<\alpha, \beta<90°$
$\sin \alpha=\frac12=\sin30°$
⇒ $\alpha =30°$
$\sin \beta=\frac12=\sin30°$
⇒ $\beta=30°$
So, $\cos(\alpha+\beta)=\cos(30°+30°)=\cos60°=\frac{1}{2}$
Hence, the correct answer is $\frac12$.
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