Discussion
If \(\sin\theta-\cos\theta=\frac{\sqrt{3}-1}{2}\), then the value of θ is :
Answer: B
The value of θ is 60°.
Check the options in the left-hand side. At 60°:
\[ \begin{aligned} \sin 60^{\circ} - \cos 60^{\circ} &= \frac{\sqrt{3}}{2} - \frac{1}{2} \\ &= \frac{\sqrt{3} - 1}{2} \end{aligned} \]
That matches. At 45° the difference is 0, at 90° it is 1, and at 75° it is \(\sin 75^{\circ} - \cos 75^{\circ} = \tfrac{\sqrt{2}}{2} \approx 0.71\), whereas \(\tfrac{\sqrt{3}-1}{2} \approx 0.37\).
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