Question : $\triangle ABC$ is a right triangle. If $\angle B=90^{\circ}$ and $\tan A=\frac{1}{\sqrt{2}}$, then the value of $\sin A \cos C + \cos A \sin C$ is:
Option 1: $1$
Option 2: $2$
Option 3: $\frac{2}{3}$
Option 4: $\frac{1}{3}$
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Correct Answer: $1$
Solution : Given: $\triangle ABC$ is a right triangle with $\angle B=90^{\circ}$ So, $A + C = 90^{\circ}$ Now, $\sin A \cos C + \cos A \sin C=\sin (A + C)$ = $\sin 90^{\circ} $ = $1$ Hence, the correct answer is $1$.
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