Question : If $\theta+\phi=\frac{\pi}{2}$ and $\sin\theta=\frac{1}{2}$, then the value of $\sin\phi$ is:
Option 1: $1$
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\frac{1}{2}$
Option 4: $\frac{\sqrt{3}}{2}$
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Correct Answer: $\frac{\sqrt{3}}{2}$
Solution :
$\theta+\phi=\frac{\pi}{2}=90°$---------(i)
Also, $\sin \theta = \frac{1}{2}=\sin 30°$
$⇒\theta =30°$
Putting $\theta = 30°$ in (i), we get:
$30° + \phi=90°$
$⇒\phi=60°$
So, $\sin \phi= \sin 60° = \frac{\sqrt{3}}{2}$
Hence, the correct answer is $\frac{\sqrt{3}}{2}$.
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