Question : In a right-angled triangle $\mathrm{XYZ}$, if $\mathrm{X}=60^{\circ}$ and $\mathrm{Y}=30^{\circ}$, then find the value of $\sin (\mathrm{X}-\mathrm{Y})$.
Option 1: $\frac{3}{5}$
Option 2: $\frac{1}{2}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{2}{3}$
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Correct Answer: $\frac{1}{2}$
Solution :
Given: $\mathrm{X}=60^{\circ}$ and $\mathrm{Y}=30^{\circ}$
Then, $\sin (\mathrm{X}-\mathrm{Y})$
= $\sin(60-30)^{\circ}$
= $\sin 30^{\circ}$
= $\frac{1}2$
Hence, the correct answer is $\frac{1}2$.
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